With the growing scale of high-performance computing (HPC) systems, today and more so tomorrow, faults are a norm rather than an exception. HPC applications typically tolerate fail-stop failures under the stop-and-wait scheme, where even if only one processor fails, the whole system has to stop and wait for the recovery of the corrupted data. It is now a more-or-less accepted fact that the stop-and-wait scheme will not scale to the next generation of HPC systems. Inspired by the previous stop-and-wait algorithm-based fault tolerance (ABFT) recovery technique, we propose in this paper a nonstop fault tolerance scheme at the application level and describe its implementation. When failure occurs during the execution of applications, we do not stop to wait for the recovery of the corrupted node; instead, we replace it with the corresponding redundant node and continue the execution. At the end of execution, the correct solution can be recovered algorithmically at a very low cost. In order to implement the scheme, some new fault-tolerant features of the Message Passing Interface (MPI) have been investigated and utilized in the MPICH implementation of MPI. We also describe a case study using High Performance Linpack (HPL) with these new features and evaluate the performance of both our new scheme and ABFT recovery. Experimental results show the advantage of our new scheme over ABFT recovery even in a small scale.