This paper proposes a new approach and new techniques for on-line monitoring of concurrent programs to ensure that some of their safety properties are not violated. The techniques modify erroneous systems, which violate a certain safety property, into new systems which satisfy the safety property. It does so by adding a new layer that controls the scheduling of steps in the system. We formally characterize the relationship between the erroneous and the new system. Safety monitors for mutual-exclusion, l\ell -exclusion, and the producer-consumer tasks are presented. Proofs for the mutual-exclusion task and the l\ell -exclusion task are presented to demonstrate the applicability of our approach.