diff --git a/spec/gl-matrix/quat-spec.js b/spec/gl-matrix/quat-spec.js
index 3cba6771..62728c46 100644
--- a/spec/gl-matrix/quat-spec.js
+++ b/spec/gl-matrix/quat-spec.js
@@ -776,20 +776,23 @@ describe("quat", function() {
     });
 
     describe("equals", function() {
-        let quatC, quatD, r0, r1, r2;
+        let quatC, quatD, quatE, r0, r1, r2, r3;
         beforeEach(function() {
-            quatA = [0, 1, 2, 3];
-            quatB = [0, 1, 2, 3];
-            quatC = [1, 2, 3, 4];
+            quatA = [0, 0, 0, 1];
+            quatB = [0, 0, 0, 1];
+            quatC = [0, 1, 0, 0];
             quatD = [1e-16, 1, 2, 3];
+            quatE = [0, -1, 0, 0];
             r0 = quat.equals(quatA, quatB);
             r1 = quat.equals(quatA, quatC);
             r2 = quat.equals(quatA, quatD);
+            r3 = quat.equals(quatC, quatE);
         });
         it("should return true for identical quaternions", function() { expect(r0).toBe(true); });
         it("should return false for different quaternions", function() { expect(r1).toBe(false); });
         it("should return true for close but not identical quaternions", function() { expect(r2).toBe(true); });
-        it("should not modify quatA", function() { expect(quatA).toBeEqualish([0, 1, 2, 3]); });
-        it("should not modify quatB", function() { expect(quatB).toBeEqualish([0, 1, 2, 3]); });
+        it("should return true for identical quaternions with flipped orientation", function() { expect(r3).toBe(true); });
+        it("should not modify quatA", function() { expect(quatA).toBeEqualish([0, 0, 0, 1]); });
+        it("should not modify quatB", function() { expect(quatB).toBeEqualish([0, 0, 0, 1]); });
     });
 });
diff --git a/src/quat.js b/src/quat.js
index e1aa4061..3a8226b2 100644
--- a/src/quat.js
+++ b/src/quat.js
@@ -513,7 +513,7 @@ export function fromEuler(out, x, y, z, order = glMatrix.ANGLE_ORDER) {
       out[3] = cx * cy * cz + sx * sy * sz;
       break;
 
-    default: 
+    default:
       throw new Error('Unknown angle order ' + order);
   }
 
@@ -673,13 +673,17 @@ export const normalize = vec4.normalize;
 export const exactEquals = vec4.exactEquals;
 
 /**
- * Returns whether or not the quaternions have approximately the same elements in the same position.
+ * Returns whether or not the quaternions point approximately to the same direction.
  *
- * @param {ReadonlyQuat} a The first vector.
- * @param {ReadonlyQuat} b The second vector.
- * @returns {Boolean} True if the vectors are equal, false otherwise.
+ * Both quaternions are assumed to be unit length.
+ *
+ * @param {ReadonlyQuat} a The first unit quaternion.
+ * @param {ReadonlyQuat} b The second unit quaternion.
+ * @returns {Boolean} True if the quaternions are equal, false otherwise.
  */
-export const equals = vec4.equals;
+export function equals(a, b) {
+    return Math.abs(vec4.dot(a, b)) >= 1 - glMatrix.EPSILON;
+}
 
 /**
  * Sets a quaternion to represent the shortest rotation from one