diff --git a/internal/transport/http_util.go b/internal/transport/http_util.go
index 3613d7b64817..968d556a1f1b 100644
--- a/internal/transport/http_util.go
+++ b/internal/transport/http_util.go
@@ -196,11 +196,14 @@ func decodeTimeout(s string) (time.Duration, error) {
 	if !ok {
 		return 0, fmt.Errorf("transport: timeout unit is not recognized: %q", s)
 	}
-	t, err := strconv.ParseInt(s[:size-1], 10, 64)
+	t, err := strconv.ParseUint(s[:size-1], 10, 64)
 	if err != nil {
 		return 0, err
 	}
-	const maxHours = math.MaxInt64 / int64(time.Hour)
+	if t == 0 {
+		return 0, fmt.Errorf("transport: timeout must be positive: %q", s)
+	}
+	const maxHours = math.MaxInt64 / uint64(time.Hour)
 	if d == time.Hour && t > maxHours {
 		// This timeout would overflow math.MaxInt64; clamp it.
 		return time.Duration(math.MaxInt64), nil
diff --git a/internal/transport/http_util_test.go b/internal/transport/http_util_test.go
index 5a259d43cdc2..546e8e7f39dc 100644
--- a/internal/transport/http_util_test.go
+++ b/internal/transport/http_util_test.go
@@ -22,28 +22,49 @@ import (
 	"errors"
 	"fmt"
 	"io"
+	"math"
 	"net"
 	"reflect"
 	"testing"
 	"time"
 )
 
-func (s) TestTimeoutDecode(t *testing.T) {
+func (s) TestDecodeTimeout(t *testing.T) {
 	for _, test := range []struct {
 		// input
 		s string
 		// output
-		d   time.Duration
-		err error
+		d       time.Duration
+		wantErr bool
 	}{
-		{"1234S", time.Second * 1234, nil},
-		{"1234x", 0, fmt.Errorf("transport: timeout unit is not recognized: %q", "1234x")},
-		{"1", 0, fmt.Errorf("transport: timeout string is too short: %q", "1")},
-		{"", 0, fmt.Errorf("transport: timeout string is too short: %q", "")},
+
+		{"00000001n", time.Nanosecond, false},
+		{"10u", time.Microsecond * 10, false},
+		{"00000010m", time.Millisecond * 10, false},
+		{"1234S", time.Second * 1234, false},
+		{"00000001M", time.Minute, false},
+		{"09999999S", time.Second * 9999999, false},
+		{"99999999S", time.Second * 99999999, false},
+		{"99999999M", time.Minute * 99999999, false},
+		{"2562047H", time.Hour * 2562047, false},
+		{"2562048H", time.Duration(math.MaxInt64), false},
+		{"99999999H", time.Duration(math.MaxInt64), false},
+		{"-1S", 0, true},
+		{"1234x", 0, true},
+		{"1234s", 0, true},
+		{"1234", 0, true},
+		{"1", 0, true},
+		{"", 0, true},
+		{"9a1S", 0, true},
+		{"0S", 0, true}, // PROTOCOL-HTTP2.md requires positive integers
+		{"00000000S", 0, true},
+		{"000000000S", 0, true},
 	} {
 		d, err := decodeTimeout(test.s)
-		if d != test.d || fmt.Sprint(err) != fmt.Sprint(test.err) {
-			t.Fatalf("timeoutDecode(%q) = %d, %v, want %d, %v", test.s, int64(d), err, int64(test.d), test.err)
+		gotErr := err != nil
+		if d != test.d || gotErr != test.wantErr {
+			t.Errorf("timeoutDecode(%q) = %d, %v, want %d, wantErr=%v",
+				test.s, int64(d), err, int64(test.d), test.wantErr)
 		}
 	}
 }