diff --git a/gzip/gunzip.go b/gzip/gunzip.go
index 4d7018913e..66fe5ddf72 100644
--- a/gzip/gunzip.go
+++ b/gzip/gunzip.go
@@ -252,42 +252,40 @@ func (z *Reader) Read(p []byte) (n int, err error) {
 		return 0, z.err
 	}
 
-	n, z.err = z.decompressor.Read(p)
-	z.digest = crc32.Update(z.digest, crc32.IEEETable, p[:n])
-	z.size += uint32(n)
-	if z.err != io.EOF {
-		// In the normal case we return here.
-		return n, z.err
-	}
+	for n == 0 {
+		n, z.err = z.decompressor.Read(p)
+		z.digest = crc32.Update(z.digest, crc32.IEEETable, p[:n])
+		z.size += uint32(n)
+		if z.err != io.EOF {
+			// In the normal case we return here.
+			return n, z.err
+		}
 
-	// Finished file; check checksum and size.
-	if _, err := io.ReadFull(z.r, z.buf[:8]); err != nil {
-		z.err = noEOF(err)
-		return n, z.err
-	}
-	digest := le.Uint32(z.buf[:4])
-	size := le.Uint32(z.buf[4:8])
-	if digest != z.digest || size != z.size {
-		z.err = ErrChecksum
-		return n, z.err
-	}
-	z.digest, z.size = 0, 0
+		// Finished file; check checksum and size.
+		if _, err := io.ReadFull(z.r, z.buf[:8]); err != nil {
+			z.err = noEOF(err)
+			return n, z.err
+		}
+		digest := le.Uint32(z.buf[:4])
+		size := le.Uint32(z.buf[4:8])
+		if digest != z.digest || size != z.size {
+			z.err = ErrChecksum
+			return n, z.err
+		}
+		z.digest, z.size = 0, 0
 
-	// File is ok; check if there is another.
-	if !z.multistream {
-		return n, io.EOF
-	}
-	z.err = nil // Remove io.EOF
+		// File is ok; check if there is another.
+		if !z.multistream {
+			return n, io.EOF
+		}
+		z.err = nil // Remove io.EOF
 
-	if _, z.err = z.readHeader(); z.err != nil {
-		return n, z.err
+		if _, z.err = z.readHeader(); z.err != nil {
+			return n, z.err
+		}
 	}
 
-	// Read from next file, if necessary.
-	if n > 0 {
-		return n, nil
-	}
-	return z.Read(p)
+	return n, nil
 }
 
 // Support the io.WriteTo interface for io.Copy and friends.