diff --git a/bignum.c b/bignum.c
index c9f2d4e4..eaed306f 100644
--- a/bignum.c
+++ b/bignum.c
@@ -568,7 +568,8 @@ sexp sexp_bignum_quot_rem (sexp ctx, sexp *rem, sexp a, sexp b) {
     }
   }
   /* adjust signs */
-  if (sign < 0) {
+  a1 = sexp_bignum_normalize(a1);
+  if (sign < 0 && a1 != SEXP_ZERO) {
     q = sexp_sub(ctx, q, SEXP_ONE);
     a1 = sexp_add(ctx, a1, b1);
   }
diff --git a/lib/chibi/numeric-test.sld b/lib/chibi/numeric-test.sld
index 79b24a9b..ef2184b5 100644
--- a/lib/chibi/numeric-test.sld
+++ b/lib/chibi/numeric-test.sld
@@ -337,5 +337,13 @@
       (let ((r  (/ (expt 2 61) 3)))
         (test 0 (- r r))
         (test 2305843009213693952/3 r))
+      (let ((x (+ (expt 2 32) +2))
+            (y (+ (expt 2 32) -1)))
+        (test 0(remainder (* x y) y))
+        (test 0(remainder (* x y) x)))
+      (let ((x (+ (expt 2 64) +2))
+            (y (+ (expt 2 64) -1)))
+        (test 0(remainder (* x y) y))
+        (test 0(remainder (* x y) x)))
 
       (test-end))))