diff --git a/pdfminer/converter.py b/pdfminer/converter.py
index d559e71c..8e627167 100644
--- a/pdfminer/converter.py
+++ b/pdfminer/converter.py
@@ -268,7 +268,7 @@ def paint_path(self, gstate, stroke, fill, evenodd, path):
         return
 
 
-class HTMLConverter(PDFConverter[BinaryIO]):
+class HTMLConverter(PDFConverter[AnyIO]):
     RECT_COLORS = {
         'figure': 'yellow',
         'textline': 'magenta',
@@ -285,7 +285,7 @@ class HTMLConverter(PDFConverter[BinaryIO]):
 
     def __init__(self,
                  rsrcmgr: PDFResourceManager,
-                 outfp: BinaryIO,
+                 outfp: AnyIO,
                  codec: str = 'utf-8',
                  pageno: int = 1,
                  laparams: Optional[LAParams] = None,
@@ -300,6 +300,11 @@ def __init__(self,
                  text_colors: Optional[Dict[str, str]] = None):
         PDFConverter.__init__(self, rsrcmgr, outfp, codec=codec, pageno=pageno,
                               laparams=laparams)
+
+        # write() assumes a codec for binary I/O, or no codec for text I/O.
+        if self.outfp_binary == (not self.codec):
+            raise ValueError("Codec is required for a binary I/O output")
+
         if text_colors is None:
             text_colors = {'char': 'black'}
         if rect_colors is None:
@@ -323,8 +328,10 @@ def __init__(self,
         return
 
     def write(self, text: str) -> None:
-        textb = text.encode(self.codec)
-        self.outfp.write(textb)
+        if self.codec:
+            cast(BinaryIO, self.outfp).write(text.encode(self.codec))
+        else:
+            cast(TextIO, self.outfp).write(text)
         return
 
     def write_header(self) -> None:
diff --git a/pdfminer/high_level.py b/pdfminer/high_level.py
index 5c5921b1..06b30645 100644
--- a/pdfminer/high_level.py
+++ b/pdfminer/high_level.py
@@ -83,10 +83,9 @@ def extract_text_to_fp(inf: BinaryIO,
                               stripcontrol=strip_control)
 
     elif output_type == 'html':
-        # Binary I/O is required, but we have no good way to test it here.
-        device = HTMLConverter(rsrcmgr, cast(BinaryIO, outfp), codec=codec,
-                               scale=scale, layoutmode=layoutmode,
-                               laparams=laparams, imagewriter=imagewriter)
+        device = HTMLConverter(rsrcmgr, outfp, codec=codec, scale=scale,
+                               layoutmode=layoutmode, laparams=laparams,
+                               imagewriter=imagewriter)
 
     elif output_type == 'tag':
         # Binary I/O is required, but we have no good way to test it here.