diff --git a/onnxscript/rewriter/rules/common/_fuse_relus_clips.py b/onnxscript/rewriter/rules/common/_fuse_relus_clips.py
index 5d294cdbd7..b47d2d9b6f 100644
--- a/onnxscript/rewriter/rules/common/_fuse_relus_clips.py
+++ b/onnxscript/rewriter/rules/common/_fuse_relus_clips.py
@@ -74,7 +74,9 @@ def extract_min_max(self, node: ir.Node):
                 min_clip = min_input.const_value.numpy()
 
         if len(node.inputs) > 2:
-            max_clip = node.inputs[2].const_value.numpy()
+            max_clip = node.inputs[2]
+            if max_clip is not None:
+                max_clip = max_clip.const_value.numpy()
 
         return min_clip, max_clip, dtype
 
diff --git a/onnxscript/rewriter/rules/common/_fuse_relus_clips_test.py b/onnxscript/rewriter/rules/common/_fuse_relus_clips_test.py
index df2d669930..0d36f19ce4 100644
--- a/onnxscript/rewriter/rules/common/_fuse_relus_clips_test.py
+++ b/onnxscript/rewriter/rules/common/_fuse_relus_clips_test.py
@@ -9,12 +9,7 @@
 import parameterized
 from onnx_ir.passes.common import onnx_checker, shape_inference
 
-from onnxscript.rewriter import (
-    MatchingTracer,
-    MatchStatus,
-    RewriteRule,
-    testing,
-)
+from onnxscript.rewriter import MatchingTracer, MatchStatus, RewriteRule, testing
 from onnxscript.rewriter.rules.common import _fuse_relus_clips
 from onnxscript.rewriter.rules.common._fuse_relus_clips import (
     successive_clip_relu_rule,
@@ -206,6 +201,35 @@ def test_successful_fuse_successive_relu_clip_no_min(self, _, nodes):
         """)
         self.run_test(model, expected_op_types=["Clip"])
 
+    @parameterized.parameterized.expand(
+        [
+            (
+                "relu_then_clip",
+                """
+                    x1 = Relu(X)
+                    Y = Clip(x1,min,"")
+                """,
+            ),
+            (
+                "clip_then_relu",
+                """
+                    x1 = Clip(X,min,"")
+                    Y = Relu(x1)
+                """,
+            ),
+        ]
+    )
+    def test_successful_fuse_successive_relu_clip_no_max(self, _, nodes):
+        model = ir.from_onnx_text(f"""
+            < ir_version: 10, opset_import: ["" : 20] >
+            test_model (float[N, 32, 14] X) => (float [N, ?, ?] Y)
+            <float min = {{1.0}}>
+            {{
+                {nodes}
+            }}
+        """)
+        self.run_test(model, expected_op_types=["Clip"])
+
     @parameterized.parameterized.expand(
         [
             (