A technique is disclosed for generating nonrandom combinatorial libraries on solid phase supports in which each of a set of predetermined species of test compounds is present on a predetermined number of solid phase supports, preferably on only one, and each solid phase support has only a single species of test compound. Each of the predetermined species of test compounds is prepared with absolute certainty because the technique does not employ any random division of the solid phase supports. Rather, the method is based on the stepwise division of a continuous solid phase support matrix prior to each synthetic step in which more than one type of subunit is added. Non-limiting examples of matrices of the solid phase supports include polypropylene membranes, polytetrafluoropropylene membranes and cotton thread. The combinatorial libraries made by the technique are also disclosed.