diff --git a/nanovllm/layers/layernorm.py b/nanovllm/layers/layernorm.py
index 71bf4198f..a969fd903 100755
--- a/nanovllm/layers/layernorm.py
+++ b/nanovllm/layers/layernorm.py
@@ -21,7 +21,7 @@ def rms_forward(
         orig_dtype = x.dtype
         x = x.float()
         var = x.pow(2).mean(dim=-1, keepdim=True)
-        x.mul_(torch.rsqrt(var + self.eps))
+        x = x * torch.rsqrt(var + self.eps)
         x = x.to(orig_dtype).mul_(self.weight)
         return x
 
diff --git a/test/test_layernorm.py b/test/test_layernorm.py
new file mode 100644
index 000000000..c4eeba986
--- /dev/null
+++ b/test/test_layernorm.py
@@ -0,0 +1,23 @@
+import importlib.util
+from pathlib import Path
+
+import torch
+
+
+spec = importlib.util.spec_from_file_location(
+    "layernorm",
+    Path(__file__).parents[1] / "nanovllm" / "layers" / "layernorm.py",
+)
+layernorm = importlib.util.module_from_spec(spec)
+spec.loader.exec_module(layernorm)
+RMSNorm = layernorm.RMSNorm
+
+
+def test_rms_norm_does_not_modify_fp32_input():
+    norm = RMSNorm(4)
+    x = torch.randn(2, 4, dtype=torch.float32)
+    expected = x.clone()
+
+    norm(x)
+
+    torch.testing.assert_close(x, expected)