KdV recursion relations for the two-matrix models

We find a KdV recursion relation for the two-matrix models in addition to that by Dijkgraaf and Witten [Nucl. Phys. B 342 (1990) 486]. We show that together the relations can be used as algebraic resursion relations for correlation functions which express all correlation functions with an insertion of P in each genus in terms of 〈PP〉, 〈PQ〉, and 〈QQ〉 in a unique way. P and Q are the puncture operator and the dilation operator, and also we assume the scaling ansatz. The KdV recursion relations found do not involve explicitly the infinite number of coupling constants as in the case of the recursion relations given by the Virasoro constraints and the W-constraints.