diff --git a/include/mcl/ec.hpp b/include/mcl/ec.hpp
index 4a29cfa..e1db56d 100644
--- a/include/mcl/ec.hpp
+++ b/include/mcl/ec.hpp
@@ -227,6 +227,12 @@ template<class E>
 bool isEqualJacobi(const E& P1, const E& P2)
 {
 	typedef typename E::Fp F;
+	bool zero1 = P1.isZero();
+	bool zero2 = P2.isZero();
+	if (zero1) {
+		return zero2;
+	}
+	if (zero2) return false;
 	F s1, s2, t1, t2;
 	F::sqr(s1, P1.z);
 	F::sqr(s2, P2.z);
@@ -452,6 +458,12 @@ template<class E>
 bool isEqualProj(const E& P1, const E& P2)
 {
 	typedef typename E::Fp F;
+	bool zero1 = P1.isZero();
+	bool zero2 = P2.isZero();
+	if (zero1) {
+		return zero2;
+	}
+	if (zero2) return false;
 	F t1, t2;
 	F::mul(t1, P1.x, P2.z);
 	F::mul(t2, P2.x, P1.z);
diff --git a/test/ec_test.cpp b/test/ec_test.cpp
index 4c93e42..a3e79e5 100644
--- a/test/ec_test.cpp
+++ b/test/ec_test.cpp
@@ -95,6 +95,9 @@ struct Test {
 			if (Ec::getMode() != mcl::ec::Affine) {
 				CYBOZU_TEST_ASSERT(!R.isNormalized());
 			}
+			CYBOZU_TEST_ASSERT(O == O);
+			CYBOZU_TEST_ASSERT(R != O);
+			CYBOZU_TEST_ASSERT(O != R);
 			CYBOZU_TEST_ASSERT(R.isValid());
 			Ec R2 = P + P;
 			CYBOZU_TEST_EQUAL(R, R2);