diff --git a/uniuri.go b/uniuri.go
index 0e9ee1b..dad8559 100644
--- a/uniuri.go
+++ b/uniuri.go
@@ -56,7 +56,7 @@ func NewLenChars(length int, chars []byte) string {
 			panic("error reading from random source: " + err.Error())
 		}
 		for _, c := range r {
-			if c > maxrb {
+			if maxrb > 0 && c > maxrb {
 				// Skip this number to avoid modulo bias.
 				continue
 			}
diff --git a/uniuri_test.go b/uniuri_test.go
index ff9a83d..b242e29 100644
--- a/uniuri_test.go
+++ b/uniuri_test.go
@@ -50,4 +50,9 @@ func TestNewLenChars(t *testing.T) {
 	}
 	// Check that only allowed characters are present
 	validateChars(t, u, chars)
+	// Check that two generated strings are different
+	u2 := NewLenChars(length, chars)
+	if u == u2 {
+		t.Fatalf("not unique: %q and %q", u, u2)
+	}
 }