The Chandy-Lamport checkpointing algorithm is widely used in fault tolerant implementations of MPI. However, it assumes the FIFO property of message passing, which is not guaranteed by the MPI standard at the application level. Therefore, this algorithm cannot serve as a basis for an implementation-independent fault tolerant MPI.In this paper, we present a variant of the Chandy-Lamport algorithm that does not rely on the FIFO property. This algorithm can be implemented on top of MPI and, hence, used for development of a supplement software component enabling the fault tolerance of any MPI implementation compliant with the MPI standard. We prove the correctness of the algorithm and analyze its performance. Experimental results demonstrating the efficiency of the algorithm are also presented.