This paper explores the use of a sub-block decomposition strategy for parallel sparse cholesky factorization, in which the sparse matrix is decomposed into rectangular blocks. Such a strategy has enormous theoretical scalability advantages over more traditional columm-oriented and panel-oriented decompositions. However, little progress has been made in producing a practical sub-block method. This paper propose and evaluates an approach that is simple to implement, provides slightly hegher performance than colum (and panel) methods on small parallel machines, and has potential to provide much higher performance on large parallel machines