The ATM switching scheme we propose is similar to the multi-frame Stop-and-Go, except that we use the EDF (Earliest-Deadline-First) scheduler, instead of the rate-monotonic, static-priority scheduler. Unlike the multi-frame Stop-and-Go, our scheme can fully utilize the link bandwidth, and does not require that the input or output frames of the same size be synchronized. EDF scheduling is, in general, more complex than static-priority scheduling. However, we show that the next earliest deadline needs to be computed only when an output frame reaches its end, i.e., not whenever a cell is output, resulting in significant saving in computation time. We show a detailed implementation, which requires two FIFO queues per frame size per switch, and derive bounds on end-to-end delay and delay-jitters.