We present a new parallel algorithm for the exact diagonalization of the t−t′-Hubbard model with the Lanczos method. By invoking a new scheme of labeling the states we were able to obtain a speedup of up to four on 16 nodes of an IBM SP2 for the calculation of the ground state energy and an almost linear speedup for the calculation of the correlation functions. Using this algorithm we performed an extensive study of the influence of the next-nearest hopping parameter t′ in the t−t′-Hubbard model on ground state energy and the superconducting correlation functions for both attractive and repulsive interaction.