In this paper we deal with totally self-checking (TSC) synchronous sequential circuits (SSCs), that are able to recover after an occurrence of a fault. We call SSC owing this property as a self-healing SSC. A concept of a partially monotonic SSC is used in the paper. It is shown that the partially monotonic SSCs satisfy the self-healing property. A novel reduced m-out-of-n code is developed. It is proposed applying this code to the synthesis of a TSC checker for the state monotonic SSCs. The proposed method of synthesis is based on a LUT implementation of monotonic functions. For most circuits in a standard benchmark set, the proposed approach leads to a reduction of about 10-20% of the overhead as compared with the traditional methods.