Relaxed encryption framework which extends hash functions of Merkle-Damg?rd construction to a parallel construction can improve Hash performance by multi-core processor. A proving process was given to show that relaxed encryption framework has no property of collision resistance when processing messages of different size. A new parallel extending algorithm was proposed base on the design of relaxed encryption framework, which remedies the security flaws of the relaxed encryption framework, and the security of the new parallel Hash construction was also discussed. The cryptanalysis shows that the property of collision resistance of the new parallel construction is not weaker than the hash function of Merkle-Damg?rd construction. Experimental results indicate that the new Hash construction performs better when processing messages of large size.