The functional decomposition of binary and multi-valued discrete functions and relations has been gaining more and more recognition. It has important applications in many fields of modern digital system engineering, such as combinational and sequential logic synthesis for VLSI systems, pattern analysis, knowledge discovery, machine learning, decision systems, data bases, data mining etc. However, its practical usefulness for very complex systems has been limited by the lack of an effective and efficient method for selecting the appropriate input supports for sub-systems. In this paper, a new effective and efficient functional decomposition method is proposed and discussed. This method is based on applying information relationship measures to input support selection. Using information relationship measures allows us to reduce the search space to a manageable size while retaining high-quality solutions in the reduced space. Experimental results demonstrate that the proposed method is able to construct optimal or near-optimal supports very efficiently, even for large systems. It is many times faster than the systematic support selection method, but delivers results of comparable quality.