The hypercube as a parallel interconnection network has been of academic and engineering concern for tens of year due to its many merits. However, its increasing node degree is an obvious weakness. Some networks such as the cube-connected cycles (CCC) and the de Bruijn network have been proposed to overcome the increasing degree of the hypercube. In this paper, we present a new cost-effective network which outperforms the cube network. It can overcome the increasing degree of cube networks while keeping the advantages of the cube network such as logarithmic diameter, easy routing, optimal fault tolerance, and suitability for the ASCEND/DESCEND class of parallel problems. Furthermore, the proposed network achieves the logarithmic diameter with a very small constant node degree, 3 or 4.