diff --git a/convert-hf-to-gguf.py b/convert-hf-to-gguf.py
index 7e601170e..37af6328a 100755
--- a/convert-hf-to-gguf.py
+++ b/convert-hf-to-gguf.py
@@ -160,7 +160,7 @@ class Model(ABC):
                 data = data.astype(np.float32)
 
             # TODO: Why cant we use these float16 as-is? There should be not reason to store float16 as float32
-            if self.ftype == 1 and data_dtype == np.float16 and n_dims == 1:
+            if self.ftype == 1 and data_dtype == np.float16 and (n_dims == 1 or new_name.endswith("_norm.weight")):
                 data = data.astype(np.float32)
 
             # if f16 desired, convert any float32 2-dim weight tensors to float16