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In the area of high-performance computation, direct methods for solving large systems of equations on distributed memory machines is one very important issue. In general, there are two ways to improve the computational efficiency of the solution procedure. One is to increase the sequential efficiency by maximizing vector operations and/or using other techniques, such as unrolling. The other is to decrease the communication cost across processors. Conventionally, the pure JIK form of LDLT factorization algorithms based on the column skyline storage scheme lead to natural synchronization, i.e., starting a step, all but one processor waits for the result of a particular processor for the j-th column or j-th block. Carefully rearranging the communication order, this paper proposes a mixed JIK form with one-step overshoot for sending and receiving. Associated with asynchronous communication, the mixed asynchronous approach can greatly reduce the processor idling time and enhance therefore the performance of parallel computation. Several practical examples show the efficiency of this approach.