This document describes a novel steganographic method for hiding data in JPEG images. It proposes improvements to the existing matrix encoding (F5) technique. Specifically, it introduces overlapped matrix encoding, modified matrix encoding using 2 or 3 coefficient flips instead of 1, and an insert-remove approach. Experimental results show this method achieves higher data hiding capacity while decreasing detectability compared to the original F5 technique according to steganalysis using 274 features.