In a distributed computing environment, it is necessary to handle the multiple processor failures. In this paper we present a new diskless checkpointing approach which combines neighbor based diskless checkpointing and parity-based diskless checkpointing. As we are storing checkpoint in the peer processors memory, the problem of stable storage is overcome by using neighbor-based diskless checkpointing method. Also for reducing memory consumption problem we use parity-based diskless checkpointing technique. There is no need of dedicated checkpoint processors. It can handle multiple processor failures simultaneously in the system.