A traffic assignment method is discussed with which the separation of passenger car link flows and truck link flows becomes possible. By considering the multi-class traffic flows (cars and trucks) as two single class traffic flows and establishing a BPR type link performance function with asymmetric interaction between cars and trucks, we are able to show a sufficient condition to get a unique solution for this problem. Then a numerical experiment is performed to test the applicability of the diagonalization algorithm to the problem, and the convergence and effectiveness of the algorithm are shown.