It has been shown that virtual output queuing (VOQ) and a sophisticated scheduling algorithm enable an input-queued switch to achieve 100% throughput for independent arrival process. Several of the scheduling algorithms that have been proposed can be classified as either iterative scheduling algorithms or symmetric crossbar arbitration algorithms. i-OCF (oldest-cell-first) and TSA (two step arbiter) are well-known examples of iterative scheduling algorithms and symmetric crossbar arbitration algorithms, respectively. However, there are drawbacks in using these algorithms. i-OCF takes long time to find completely a conflict-free match between input ports and output ports because it requires multiple iterations. If i-OCF cannot find a conflict-free match completely, the switch throughput falls. TSA has the possibility that it finds a conflict-free match faster than i-OCF because it does not need any iterations. However, TSA suffers from the starvation problem. In this paper, we propose a new scheduling algorithm. It uses two schedulers, which we call scheduler 1 and scheduler 2, in parallel. After cells were transmitted, the information that input port i granted the offer from output port j in scheduler 2 is mapped to scheduler 1 if and only if input port i has at least one cell destined for output port j. If the information is moved, input port i and output port j are matched in scheduler 1 at the beginning of the next time slot. Our proposed algorithm uses one scheduler based on TSA and the other scheduler based on i-OCF. Numerical results show that the proposed scheduling algorithm does not require multiple iterations to find a conflict-free match completely and suffer from the starvation problem for both uniform and bursty traffic.