In this paper, we present a novel, fast algorithm for allocating the transmit power to the secondary users (SUs) to maximize the total SU throughput in a cognitive radio network (CRN) while maintaining interference to the primary user (PU) within an acceptable range. The problem is formulated so as to apply Karush-Kuhn-Tucker (KKT) conditions to derive a fast, low complexity algorithm which requires less number of floating point operations. The performance of the proposed algorithm is verified by simulations. © 2018 IEEE.