We present a new scheduling algorithm for task graphs arising from parallel multifrontal methods for sparse linear systems. This algorithm is based on the theorem proved by Prasanna and Musicus [1] for tree-shaped task graphs, when all tasks exhibit the same degree of parallelism. We propose extended versions of this algorithm to take communication between tasks and memory balancing into account. The efficiency of proposed approach is assessed by a set of experiments on a set of large sparse matrices from several libraries.