diff --git a/src/functions/shamir_secret_sharing.js b/src/functions/shamir_secret_sharing.js
index def4f16..6d5688a 100644
--- a/src/functions/shamir_secret_sharing.js
+++ b/src/functions/shamir_secret_sharing.js
@@ -126,13 +126,14 @@ module.exports = function (S) {
             let q = [secret[b]];
 
             for (let i = 0; i < threshold - 1; i++) {
+                let isLeadingCoefficient = i === threshold - 2;
                 do {
                     if (ePointer >= e.length) {
                         ePointer = 0;
                         e = S.generateEntropy({hex:false});
                     }
                     w  = e[ePointer++];
-                } while (q.includes(w));
+                } while (q.includes(w) || (isLeadingCoefficient && w === 0));
                 q.push(w);
             }
 
@@ -167,4 +168,4 @@ module.exports = function (S) {
     };
 
     S.__precompute_GF256_expLog(S);
-};
\ No newline at end of file
+};
diff --git a/test/jsbtc.test.js b/test/jsbtc.test.js
index 99a4ce8..b0ad69b 100644
--- a/test/jsbtc.test.js
+++ b/test/jsbtc.test.js
@@ -580,6 +580,28 @@ describe(`${(browser) ? 'Browser' : 'Node'} test jsbtc library`, function () {
 
             }
         }).timeout(14000);
+
+        it('Secret splitting rejects zero leading coefficients', () => {
+            let originalGenerateEntropy = window.generateEntropy;
+            let entropyChunks = [
+                Buffer.from([1, 2, 3]),
+                Buffer.from([7, 0, 11])
+            ];
+            try {
+                window.generateEntropy = () => entropyChunks.shift() || Buffer.from([11]);
+                let secret = Buffer.from([42]);
+                let shares = __split_secret(3, 3, secret);
+                let keys = Object.keys(shares);
+                let twoShares = {};
+                twoShares[keys[0]] = shares[keys[0]];
+                twoShares[keys[1]] = shares[keys[1]];
+
+                assert.notEqual(__restore_secret(twoShares)[0], secret[0]);
+                equal(__restore_secret(shares)[0], secret[0]);
+            } finally {
+                window.generateEntropy = originalGenerateEntropy;
+            }
+        });
     });
 
     describe("Private/Public key functions:", function () {
@@ -2926,4 +2948,3 @@ describe(`${(browser) ? 'Browser' : 'Node'} test jsbtc library`, function () {
 
 
 });
-