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A multiple-output function can be represented by a binary decision diagram for characteristic function (BDD_for_CF). This paper presents a new method to represent multiple-output incompletely specified functions using BDD_for_CF. An algorithm to reduce the widths of BDD_for_CFs is presented. This method is useful for decomposition of incompletely specified multiple-output functions. Experimental results for radix converters, adders and a multiplier show that this method is useful for the synthesis of LUT cascades. This data structure is also useful to three-valued logic simulation.