This paper describes the block coding algorithm that underpins the new High Throughput JPEG 2000 (HTJ2K) standard. The objective of HTJ2K is to overcome the computational complexity of the original block coding algorithm, by providing a drop-in replacement that preserves as much of the JPEG 2000 feature set as possible, while allowing reversible transcoding to/from the original format. We show how the new standard achieves these goals, with high coding efficiency, and extremely high throughput in software.