diff --git a/onnxscript/function_libs/torch_lib/ops/linalg.py b/onnxscript/function_libs/torch_lib/ops/linalg.py
index 05bac181ca..c9d870bd86 100644
--- a/onnxscript/function_libs/torch_lib/ops/linalg.py
+++ b/onnxscript/function_libs/torch_lib/ops/linalg.py
@@ -330,8 +330,9 @@ def aten_linalg_vector_norm(
         keepdim = False
     else:
         dim = op.Reshape(dim, op.Constant(value_ints=[-1]))
-    self = op.Abs(self)
+
     if math.isinf(ord):
+        self = op.Abs(self)
         if ord > 0:
             return op.ReduceMax(self, dim, keepdims=keepdim)
         else:
@@ -345,6 +346,9 @@ def aten_linalg_vector_norm(
     elif ord == 2.0:
         return op.ReduceL2(self, dim, keepdims=keepdim)
     else:
+        if ord < 0 or ord % 2 != 0:
+            # Not an even integer (could be odd, fractional or negative), use Abs
+            self = op.Abs(self)
         self_pow = op.Pow(self, ord)
         exp = op.CastLike(1 / ord, self)
         return op.Pow(op.ReduceSum(self_pow, dim, keepdims=keepdim), exp)