diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h
index fd14bf1..490982b 100644
--- a/src/ecmult_impl.h
+++ b/src/ecmult_impl.h
@@ -607,6 +607,19 @@ static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) {
         } else {
             wnaf[pos] = (val + sign) ^ sign;
         }
+        /* Set a coefficient to zero if it is 1 or -1 and the proceeding digit
+         * is strictly negative or strictly positive respectively. Only change
+         * coefficients at previous positions because above code assumes that
+         * wnaf[pos - 1] is odd.
+         */
+        if (pos >= 2 && ((wnaf[pos - 1] == 1 && wnaf[pos - 2] < 0) || (wnaf[pos - 1] == -1 && wnaf[pos - 2] > 0))) {
+            if (wnaf[pos - 1] == 1) {
+                wnaf[pos - 2] += 1 << w;
+            } else {
+                wnaf[pos - 2] -= 1 << w;
+            }
+            wnaf[pos - 1] = 0;
+        }
         ++pos;
     }
     VERIFY_CHECK(pos == WNAF_SIZE(w));
diff --git a/src/tests.c b/src/tests.c
index 893d297..ed88811 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -3022,8 +3022,7 @@ void test_fixed_wnaf(const secp256k1_scalar *number, int w) {
     for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
         secp256k1_scalar t;
         int v = wnaf[i];
-        CHECK(v != 0); /* check nonzero */
-        CHECK(v & 1);  /* check parity */
+        CHECK(v == 0 || v & 1);  /* check parity */
         CHECK(v > -(1 << w)); /* check range above */
         CHECK(v < (1 << w));  /* check range below */