diff --git a/alu_u32/src/com/stark.rs b/alu_u32/src/com/stark.rs
index 3dff54ef..9ce13575 100644
--- a/alu_u32/src/com/stark.rs
+++ b/alu_u32/src/com/stark.rs
@@ -35,6 +35,8 @@ where
         );
         builder.assert_bool(local.not_equal);
         builder.assert_eq(local.not_equal, local.diff * local.diff_inv);
+        let equal = AB::Expr::one() - local.not_equal;
+        builder.assert_zero(equal * local.diff);
 
         builder.assert_bool(local.is_ne);
         builder.assert_bool(local.is_eq);
diff --git a/cpu/src/stark.rs b/cpu/src/stark.rs
index def87bf2..425267bd 100644
--- a/cpu/src/stark.rs
+++ b/cpu/src/stark.rs
@@ -267,6 +267,8 @@ impl CpuChip {
         );
         builder.assert_bool(local.not_equal);
         builder.assert_eq(local.not_equal, local.diff * local.diff_inv);
+        let equal = AB::Expr::one() - local.not_equal;
+        builder.assert_zero(equal * local.diff);
     }
 }