diff --git a/torchao/prototype/spinquant/hadamard_utils.py b/torchao/prototype/spinquant/hadamard_utils.py
index f3ed3b4290..1a88664c79 100644
--- a/torchao/prototype/spinquant/hadamard_utils.py
+++ b/torchao/prototype/spinquant/hadamard_utils.py
@@ -237,7 +237,7 @@ def apply_exact_had_to_linear(module, had_dim=-1, output=False, R2=None):
         assert is_pow2(had_dim), "Hadamard dimension must be a power of 2!"
 
     W = module.weight.data
-    if module.bias is not None:
+    if output and module.bias is not None:
         B = module.bias.data
         bias_dtype_orig = B.dtype
         B = B.float()
@@ -248,12 +248,12 @@ def apply_exact_had_to_linear(module, had_dim=-1, output=False, R2=None):
         if output:
             had_K, K = get_hadK(out_features)
             W = matmul_hadU(W.t(), had_K.to(W.device), K).t()
-            if module.bias is not None:
+            if output and module.bias is not None:
                 B = matmul_hadU(B, had_K.to(B.device), K)
         else:
             had_K, K = get_hadK(in_features)
             W = matmul_hadU(W, had_K.to(W.device), K)
-            if module.bias is not None:
+            if output and module.bias is not None:
                 B = matmul_hadU(B, had_K.to(B.device), K)
     else:
         if R2 is not None:
@@ -268,7 +268,7 @@ def apply_exact_had_to_linear(module, had_dim=-1, output=False, R2=None):
         temp = W.reshape(-1, shape[-1] // had_dim, had_dim)
         temp = temp.to(torch.float64) @ hadK
         W = temp.reshape(shape)
-        if module.bias is not None:
+        if output and module.bias is not None:
             shape = B.shape
             temp = B.reshape(-1, had_dim)
             temp = temp.to(torch.float64) @ hadK
@@ -278,5 +278,5 @@ def apply_exact_had_to_linear(module, had_dim=-1, output=False, R2=None):
             W = W.t()
 
     module.weight.data = W.to(dtype=dtype_orig)
-    if module.bias is not None:
+    if output and module.bias is not None:
         module.bias.data = B.to(dtype=bias_dtype_orig)
diff --git a/torchao/prototype/tests/test_spinquant.py b/torchao/prototype/tests/test_spinquant.py
new file mode 100644
index 0000000000..f9dce4d9d6
--- /dev/null
+++ b/torchao/prototype/tests/test_spinquant.py
@@ -0,0 +1,27 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the BSD 3-Clause license found in the
+# LICENSE file in the root directory of this source tree.
+
+import unittest
+
+import torch
+import torch.nn as nn
+
+from torchao.prototype.spinquant.hadamard_utils import apply_exact_had_to_linear
+
+
+class TestSpinQuant(unittest.TestCase):
+    def test_rotate_in_and_out(self):
+        """Perform rotation to output of linear layer and inverse rotation to input of next layer; test that the output is the same."""
+        with torch.no_grad():
+            layer1 = nn.Linear(256, 256, bias=True)
+            layer2 = nn.Linear(256, 256, bias=True)
+            model = nn.Sequential(layer1, layer2)
+            input = torch.rand(256)
+            output = model(input)
+            apply_exact_had_to_linear(layer1, output=True)
+            apply_exact_had_to_linear(layer2, output=False)
+            new_output = model(input)
+            torch.testing.assert_allclose(output, new_output)