diff --git a/encoding/traditionalchinese/all_test.go b/encoding/traditionalchinese/all_test.go
index 3097827..3825c76 100644
--- a/encoding/traditionalchinese/all_test.go
+++ b/encoding/traditionalchinese/all_test.go
@@ -5,6 +5,7 @@
 package traditionalchinese
 
 import (
+	"fmt"
 	"io/ioutil"
 	"strings"
 	"testing"
@@ -28,7 +29,12 @@
 		e         encoding.Encoding
 		src, want string
 	}{
+		{dec, Big5, "\x80", "\ufffd"},
+		{dec, Big5, "\x81", "\ufffd"},
+		{dec, Big5, "\x81\x30", "\ufffd\x30"},
 		{dec, Big5, "\x81\x40", "\ufffd"},
+		{dec, Big5, "\x81\xa0", "\ufffd"},
+		{dec, Big5, "\xff", "\ufffd"},
 
 		{enc, Big5, "갂", ""},
 		{enc, Big5, "a갂", "a"},
@@ -36,14 +42,24 @@
 	}
 	for _, tc := range testCases {
 		dir, tr, wantErr := tc.init(tc.e)
-
-		dst, _, err := transform.String(tr, tc.src)
-		if err != wantErr {
-			t.Errorf("%s %v(%q): got %v; want %v", dir, tc.e, tc.src, err, wantErr)
-		}
-		if got := string(dst); got != tc.want {
-			t.Errorf("%s %v(%q):\ngot  %q\nwant %q", dir, tc.e, tc.src, got, tc.want)
-		}
+		t.Run(fmt.Sprintf("%s/%v/%q", dir, tc.e, tc.src), func(t *testing.T) {
+			dst := make([]byte, 100)
+			src := []byte(tc.src)
+			for i := 0; i <= len(tc.src); i++ {
+				nDst, nSrc, err := tr.Transform(dst, src[:i], false)
+				if err != nil && err != transform.ErrShortSrc && err != wantErr {
+					t.Fatalf("error on first call to Transform: %v", err)
+				}
+				n, _, err := tr.Transform(dst[nDst:], src[nSrc:], true)
+				nDst += n
+				if err != wantErr {
+					t.Fatalf("(%q|%q): got %v; want %v", tc.src[:i], tc.src[i:], err, wantErr)
+				}
+				if got := string(dst[:nDst]); got != tc.want {
+					t.Errorf("(%q|%q):\ngot  %q\nwant %q", tc.src[:i], tc.src[i:], got, tc.want)
+				}
+			}
+		})
 	}
 }
 
diff --git a/encoding/traditionalchinese/big5.go b/encoding/traditionalchinese/big5.go
index 275821f..1fcddde 100644
--- a/encoding/traditionalchinese/big5.go
+++ b/encoding/traditionalchinese/big5.go
@@ -5,7 +5,6 @@
 package traditionalchinese
 
 import (
-	"errors"
 	"unicode/utf8"
 
 	"golang.org/x/text/encoding"
@@ -26,8 +25,6 @@
 	identifier.Big5,
 }
 
-var errInvalidBig5 = errors.New("traditionalchinese: invalid Big5 encoding")
-
 type big5Decoder struct{ transform.NopResetter }
 
 func (big5Decoder) Transform(dst, src []byte, atEOF bool) (nDst, nSrc int, err error) {
@@ -40,8 +37,12 @@
 
 		case 0x81 <= c0 && c0 < 0xff:
 			if nSrc+1 >= len(src) {
-				err = transform.ErrShortSrc
-				break loop
+				if !atEOF {
+					err = transform.ErrShortSrc
+					break loop
+				}
+				r, size = utf8.RuneError, 1
+				goto write
 			}
 			c1 := src[nSrc+1]
 			switch {
@@ -49,9 +50,12 @@
 				c1 -= 0x40
 			case 0xa1 <= c1 && c1 < 0xff:
 				c1 -= 0x62
+			case c1 < 0x40:
+				r, size = utf8.RuneError, 1
+				goto write
 			default:
-				err = errInvalidBig5
-				break loop
+				r, size = utf8.RuneError, 2
+				goto write
 			}
 			r, size = '\ufffd', 2
 			if i := int(c0-0x81)*157 + int(c1); i < len(decode) {
@@ -80,10 +84,10 @@
 			}
 
 		default:
-			err = errInvalidBig5
-			break loop
+			r, size = utf8.RuneError, 1
 		}
 
+	write:
 		if nDst+utf8.RuneLen(r) > len(dst) {
 			err = transform.ErrShortDst
 			break loop
@@ -99,9 +103,6 @@
 		nDst += copy(dst[nDst:], s)
 		continue loop
 	}
-	if atEOF && err == transform.ErrShortSrc {
-		err = errInvalidBig5
-	}
 	return nDst, nSrc, err
 }