A desired property of large distributed systems is self adaptability against the faults that occur more frequently as the size of the distributed system grows. Self-stabilizing protocols provide autonomous recovery from finite number of transient faults. Fault-containing self-stabilizing protocols promise not only self-stabilization but also containment of faults (quick recovery and small effect) against small number of faults. However, existing composition techniques for self-stabilizing protocols (e.g. fair composition) cannot preserve the fault-containment property when composing fault-containing self-stabilizing protocols. In this paper, we present Recovery Waiting Fault-containing Composition (RWFC) framework that provides a composition of multiple fault-containing self-stabilizing protocols while preserving the fault-containment property of the source protocols.