In JPEG-LS, fixed predictor based on median edge detector (MED) only detect horizontal and vertical edges, and thus produces large prediction errors in the locality of diagonal edges. In this paper, we propose a threshold-based edge detection scheme for the fixed predictor. The proposed scheme can detect not only the horizontal and vertical edges, but also diagonal edges. For some certain thresholds, the proposed scheme can be simplified to other existing schemes. So, it can also be regarded as the integration of these existing schemes. For a suitable threshold, the accuracy of horizontal and vertical edges detection is higher than the existing median edge detection in JPEG-LS. Thus, the proposed fixed predictor outperforms the existing JPEG-LS predictors for all images tested, while the complexity of the overall algorithm is maintained at a similar level.