The authors present a method for multilevel logic minimization which is particularly suitable for the minimization of look-up table type FPGAs (field programmable gate arrays). Given a set of nodes to be minimized, one first calculates sets of supports which are necessary to construct the functions for the given nodes by applying functional reduction. The functional reduction process guarantees that one can get the minimal support for each node. One then makes a covering table for the set of nodes to be minimized so that one can get the minimal supports to cover all the functions for the given set of nodes to be minimized. The authors present a preliminary implementation and its results for ISCAS combinational benchmark circuits combined with MIS2.1 standard script and a Boolean resubstitution minimizer, and show the effectiveness of the presented method.