The watermark that restores the exact original image from the watermarked one is called reversible watermark. Firstly, the LSB data embedding method had been proposed and the variants using integer transform and wavelet transform were proposed. In this paper, a watermark is embedded into prediction errors calculated using a predictive coding technique in JPEG-LS to increase the information to be embedded with less degradation. Since the predictor is strongly dependent on the previous pixel values, a tiny change in one pixel value propagates to the following prediction values. Based on the property, we propose a secure reversible watermarking scheme such that a watermark cannot be recovered without a secret key used at the embedding operation.