This article proposes an original approach that applies the Rollback-Dependency Trackability (RDT) property to implement a new non-blocking synchronous checkpointing protocol, called RDT-NBS, that takes mutable checkpoints and efficiently supports concurrent initiators. Mutable checkpoints can be saved in non-stable storage and make it possible for non-blocking synchronous checkpointing protocols to save a minimal number of checkpoints in stable storage during the construction of a consistent global checkpoint. We prove that this minimality property does not hold in presence of concurrent checkpointing initiations. Even though, RDT-NBS uses mutable checkpoints to reduce the use of stable memory assuring the existence of a consistent global checkpoint in stable storage. We also present simulation results that compare RDT-NBS to quasisynchronous RDT.