diff --git a/contracts/utils/math/Math.sol b/contracts/utils/math/Math.sol
index 66bb22005..7280bddeb 100644
--- a/contracts/utils/math/Math.sol
+++ b/contracts/utils/math/Math.sol
@@ -25,8 +25,8 @@ library Math {
      * zero.
      */
     function average(uint256 a, uint256 b) internal pure returns (uint256) {
-        // (a + b) / 2 can overflow, so we distribute.
-        return (a / 2) + (b / 2) + (((a % 2) + (b % 2)) / 2);
+        // (a + b) / 2 can overflow.
+        return (a & b) + (a ^ b) / 2;
     }
 
     /**
diff --git a/test/utils/math/Math.test.js b/test/utils/math/Math.test.js
index 31d3e17ac..7e194dec7 100644
--- a/test/utils/math/Math.test.js
+++ b/test/utils/math/Math.test.js
@@ -54,6 +54,11 @@ contract('Math', function (accounts) {
       const b = new BN('84346');
       expect(await this.math.average(a, b)).to.be.bignumber.equal(bnAverage(a, b));
     });
+
+    it('is correctly calculated with two max uint256 numbers', async function () {
+      const a = MAX_UINT256;
+      expect(await this.math.average(a, a)).to.be.bignumber.equal(bnAverage(a, a));
+    });
   });
 
   describe('ceilDiv', function () {