Recently, among various data hiding techniques, a new subset, lossless data hiding, has drawn tremendous interests. Most of the existing lossless data hiding algorithms are, however, fragile in the sense that they will be defeated when compression or other small alteration is applied to the marked image. De Fleeschouwer et al's method is the only existing semi-fragile lossless data hiding technique (also referred to as robust lossless data hiding in this paper), which is robust against high quality JPEG compression. In this paper, we first pointed out that this technique has a fatal problem: salt-pepper noise caused by using modulo 256 addition. We then propose a novel robust lossless data hiding technique, which does not generate salt-pepper noise. This technique has been successfully applied to many commonly used images (including medical images, more than 1000 images in CorelDRAW database and JPEG2000 test images), thus demonstrating its generality. The experimental results show that the visual quality, payload and robustness are acceptable. In addition to medical and law enforcement fields, it has been applied to authenticate losslessly compressed JPEG2000 images.