diff --git a/roaring.go b/roaring.go
index 131b1247..b78f83cc 100644
--- a/roaring.go
+++ b/roaring.go
@@ -57,11 +57,14 @@ func (rb *Bitmap) ToBytes() ([]byte, error) {
 // The format is compatible with other RoaringBitmap
 // implementations (Java, C) and is documented here:
 // https://github.com/RoaringBitmap/RoaringFormatSpec
-func (rb *Bitmap) ReadFrom(reader io.Reader) (p int64, err error) {
+// Since io.Reader is regarded as a stream and cannot be read twice.
+// So add cookieHeader to accept the 4-byte data that has been read in roaring64.ReadFrom.
+// It is not necessary to pass cookieHeader when call roaring.ReadFrom to read the roaring32 data directly.
+func (rb *Bitmap) ReadFrom(reader io.Reader, cookieHeader ...byte) (p int64, err error) {
 	stream := internal.ByteInputAdapterPool.Get().(*internal.ByteInputAdapter)
 	stream.Reset(reader)
 
-	p, err = rb.highlowcontainer.readFrom(stream)
+	p, err = rb.highlowcontainer.readFrom(stream, cookieHeader...)
 	internal.ByteInputAdapterPool.Put(stream)
 
 	return
diff --git a/roaring64/roaring64.go b/roaring64/roaring64.go
index 15651b27..21a1535e 100644
--- a/roaring64/roaring64.go
+++ b/roaring64/roaring64.go
@@ -11,6 +11,9 @@ import (
 	"github.com/RoaringBitmap/roaring"
 )
 
+const serialCookieNoRunContainer = 12346 // only arrays and bitmaps
+const serialCookie = 12347               // runs, arrays, and bitmaps
+
 // Bitmap represents a compressed bitmap where you can add integers.
 type Bitmap struct {
 	highlowcontainer roaringArray64
@@ -79,16 +82,23 @@ func (rb *Bitmap) WriteTo(stream io.Writer) (int64, error) {
 // implementations (Java, C) and is documented here:
 // https://github.com/RoaringBitmap/RoaringFormatSpec
 func (rb *Bitmap) ReadFrom(stream io.Reader) (p int64, err error) {
-
+	cookie, r32, p, err := tryReadFromRoaring32(rb, stream)
+	if err != nil {
+		return p, err
+	} else if r32 {
+		return p, nil
+	}
 	// TODO: Add buffer interning as in base roaring package.
 
-	sizeBuf := make([]byte, 8)
+	sizeBuf := make([]byte, 4)
 	var n int
 	n, err = stream.Read(sizeBuf)
 	if n == 0 || err != nil {
 		return int64(n), fmt.Errorf("error in bitmap.readFrom: could not read number of containers: %s", err)
 	}
 	p += int64(n)
+	sizeBuf = append(cookie, sizeBuf...)
+
 	size := binary.LittleEndian.Uint64(sizeBuf)
 	rb.highlowcontainer = roaringArray64{}
 	rb.highlowcontainer.keys = make([]uint32, size)
@@ -113,6 +123,30 @@ func (rb *Bitmap) ReadFrom(stream io.Reader) (p int64, err error) {
 	return p, nil
 }
 
+func tryReadFromRoaring32(rb *Bitmap, stream io.Reader) (cookie []byte, r32 bool, p int64, err error) {
+	// Verify the first two bytes are a valid MagicNumber.
+	cookie = make([]byte, 4)
+	size, err := stream.Read(cookie)
+	if err != nil {
+		return cookie, false, int64(size), err
+	}
+	fileMagic := int(binary.LittleEndian.Uint16(cookie[0:2]))
+	if fileMagic == serialCookieNoRunContainer || fileMagic == serialCookie {
+		bm32 := roaring.NewBitmap()
+		p, err = bm32.ReadFrom(stream, cookie...)
+		if err != nil {
+			return
+		}
+		rb.highlowcontainer = roaringArray64{
+			keys:            []uint32{0},
+			containers:      []*roaring.Bitmap{bm32},
+			needCopyOnWrite: []bool{false},
+		}
+		return cookie, true, p, nil
+	}
+	return
+}
+
 // FromBuffer creates a bitmap from its serialized version stored in buffer
 // func (rb *Bitmap) FromBuffer(data []byte) (p int64, err error) {
 //
diff --git a/roaring64/roaring64_test.go b/roaring64/roaring64_test.go
index de8ce556..b5d92ff1 100644
--- a/roaring64/roaring64_test.go
+++ b/roaring64/roaring64_test.go
@@ -2,9 +2,12 @@ package roaring64
 
 import (
 	"fmt"
+	"io/ioutil"
 	"log"
 	"math"
 	"math/rand"
+	"os"
+	"path/filepath"
 	"strconv"
 	"testing"
 	"unsafe"
@@ -2004,3 +2007,93 @@ func IntsEquals(a, b []uint64) bool {
 	}
 	return true
 }
+
+func Test_tryReadFromRoaring32(t *testing.T) {
+	r32 := roaring.BitmapOf(1, 2, 65535, math.MaxUint32-1)
+	bs, err := r32.ToBytes()
+	if err != nil {
+		t.Fatal(err)
+	}
+	r64 := NewBitmap()
+	assert.True(t, r64.UnmarshalBinary(bs) == nil)
+	assert.True(t, r64.Contains(1))
+	assert.True(t, r64.Contains(2))
+	assert.True(t, r64.Contains(65535))
+	assert.True(t, r64.Contains(math.MaxUint32-1))
+
+}
+
+func Test_tryReadFromRoaring32_File(t *testing.T) {
+	tempDir, err := ioutil.TempDir("./", "testdata")
+	if err != nil {
+		t.Fail()
+	}
+	defer os.RemoveAll(tempDir)
+
+	r32 := roaring.BitmapOf(1, 2, 65535, math.MaxUint32-1)
+	bs, err := r32.ToBytes()
+	if err != nil {
+		t.Fatal(err)
+	}
+	name := filepath.Join(tempDir, "r32")
+	if err := ioutil.WriteFile(name, bs, 0600); err != nil {
+		t.Fatal(err)
+	}
+	file, err := os.Open(name)
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer file.Close()
+
+	r64 := NewBitmap()
+	r64.ReadFrom(file)
+	assert.True(t, r64.Contains(1))
+	assert.True(t, r64.Contains(2))
+	assert.True(t, r64.Contains(65535))
+	assert.True(t, r64.Contains(math.MaxUint32-1))
+}
+
+func Test_tryReadFromRoaring32WithRoaring64(t *testing.T) {
+	r64 := BitmapOf(1, 65535, math.MaxUint32, math.MaxUint64)
+	bs, err := r64.ToBytes()
+	if err != nil {
+		t.Fatal(err)
+	}
+	nr64 := NewBitmap()
+	assert.True(t, nr64.UnmarshalBinary(bs) == nil)
+	assert.True(t, nr64.Contains(1))
+	assert.True(t, nr64.Contains(65535))
+	assert.True(t, nr64.Contains(math.MaxUint32))
+	assert.True(t, nr64.Contains(math.MaxUint64))
+}
+
+func Test_tryReadFromRoaring32WithRoaring64_File(t *testing.T) {
+	tempDir, err := ioutil.TempDir("./", "testdata")
+	if err != nil {
+		t.Fail()
+	}
+	defer os.RemoveAll(tempDir)
+
+	r64 := BitmapOf(1, 65535, math.MaxUint32, math.MaxUint64)
+	bs, err := r64.ToBytes()
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	name := filepath.Join(tempDir, "r32")
+	if err := ioutil.WriteFile(name, bs, 0600); err != nil {
+		t.Fatal(err)
+	}
+	file, err := os.Open(name)
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer file.Close()
+
+	nr64 := NewBitmap()
+	nr64.ReadFrom(file)
+	assert.True(t, nr64.Contains(1))
+	assert.True(t, nr64.Contains(65535))
+	assert.True(t, nr64.Contains(math.MaxUint32))
+	assert.True(t, nr64.Contains(math.MaxUint64))
+}
diff --git a/roaringarray.go b/roaringarray.go
index 077695bc..4aefc6a3 100644
--- a/roaringarray.go
+++ b/roaringarray.go
@@ -549,11 +549,19 @@ func (ra *roaringArray) toBytes() ([]byte, error) {
 	return buf.Bytes(), err
 }
 
-func (ra *roaringArray) readFrom(stream internal.ByteInput) (int64, error) {
-	cookie, err := stream.ReadUInt32()
-
-	if err != nil {
-		return stream.GetReadBytes(), fmt.Errorf("error in roaringArray.readFrom: could not read initial cookie: %s", err)
+func (ra *roaringArray) readFrom(stream internal.ByteInput, cookieHeader ...byte) (int64, error) {
+  var cookie uint32
+	var err error
+  if len(cookieHeader) > 0 && len(cookieHeader) != 4 {
+		return int64(len(cookieHeader)), fmt.Errorf("error in roaringArray.readFrom: could not read initial cookie: incorrect size of cookie header")
+	}
+	if len(cookieHeader) == 4 {
+		cookie = binary.LittleEndian.Uint32(cookieHeader)
+	} else {
+		cookie, err = stream.ReadUInt32()
+		if err != nil {
+			return stream.GetReadBytes(), fmt.Errorf("error in roaringArray.readFrom: could not read initial cookie: %s", err)
+		}
 	}
 
 	var size uint32
@@ -570,7 +578,6 @@ func (ra *roaringArray) readFrom(stream internal.ByteInput) (int64, error) {
 		}
 	} else if cookie == serialCookieNoRunContainer {
 		size, err = stream.ReadUInt32()
-
 		if err != nil {
 			return stream.GetReadBytes(), fmt.Errorf("malformed bitmap, failed to read a bitmap size: %s", err)
 		}