diff --git a/crates/transpiler/src/passes/commutation_cancellation.rs b/crates/transpiler/src/passes/commutation_cancellation.rs
index 99a4b3b10ba8..fd7673e02a73 100644
--- a/crates/transpiler/src/passes/commutation_cancellation.rs
+++ b/crates/transpiler/src/passes/commutation_cancellation.rs
@@ -338,7 +338,7 @@ pub fn cancel_commutations(
                     } else if sx_supported && is_multiple_of_pi(total_angle, 0.5) {
                         let num_sx = (total_angle / FRAC_PI_2).round();
                         total_phase -= FRAC_PI_4 * num_sx;
-                        for _ in 0..(num_sx as i64) % 4 {
+                        for _ in 0..(num_sx as i64).rem_euclid(4) {
                             dag.insert_1q_on_incoming_qubit((StandardGate::SX, &[]), cancel_set[0]);
                         }
                     } else {
diff --git a/releasenotes/notes/fix-commutative-cancellation-sxdg-12c52787870c18fb.yaml b/releasenotes/notes/fix-commutative-cancellation-sxdg-12c52787870c18fb.yaml
new file mode 100644
index 000000000000..66cc4c0429b2
--- /dev/null
+++ b/releasenotes/notes/fix-commutative-cancellation-sxdg-12c52787870c18fb.yaml
@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Fixed a miscompilation in :class:`.CommutativeCancellation` when a run of single-qubit :math:`X`
+    rotations coalesced to a negative angle and :math:`\sqrt X` was available as a target gate.  See
+    `#16594 <https://github.com/Qiskit/qiskit/issues/16594>`__.
diff --git a/test/python/transpiler/test_commutative_cancellation.py b/test/python/transpiler/test_commutative_cancellation.py
index 8750d352a95d..fd6fcd8e518e 100644
--- a/test/python/transpiler/test_commutative_cancellation.py
+++ b/test/python/transpiler/test_commutative_cancellation.py
@@ -981,6 +981,19 @@ def test_determinism(self):
         # The actual asseertion.
         self.assertTrue(left.structurally_equal(right))
 
+    @ddt.data(2, 3, 4)
+    def test_negative_x_rotations(self, num_sxdg):
+        qc = QuantumCircuit(1)
+        for _ in range(num_sxdg):
+            qc.sxdg(0)
+
+        expected = qc.copy_empty_like()
+        for _ in range(4 - num_sxdg):
+            expected.sx(0)
+
+        pass_ = CommutativeCancellation(["sx", "rz"])
+        self.assertEqual(pass_(qc), expected)
+
 
 if __name__ == "__main__":
     unittest.main()