The hypercube-like interconncetion network,X-hypercubes,has the same number of nodes and edges as conventional hypercubes.By slightly changing the interconneton way between nodes,however,X-hypercubes reduces the diameter by almost half.Thus the communication delay in X-hypercubes can be expected to be much lower than that in hypercubes. This paper gives a new definition of X-hypercubes establishing clear-cut condition of connection between two nodes.As appliction examples of the new definition,this paper presents simple embeddings of hypercubes in X-hypercubes and vice versa.This means that any programs written for hypercubes can be transported onto X-hypercubes and vice versa with minimal overhead.This paper also present bitonic merge sort for X-hypercubes by simulation that for hypercubes.