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An improvement of the forced-convergence decoding algorithm is discussed. Iterative decoding schemes such as the sum-product (SP) decoding bring out excellent performance of low-density parity check (LDPC) codes. The forced-convergence (FC) decoding is also an iterative decoding algorithm obtained by modifying the SP decoding. The FC decoding succeeds to reduce the decoding complexity of the SP decoding, but the error correcting performance is severely degraded by the modification. The performance degradation of the FC decoding is expected to be mitigated if the convergence criterion used in the algorithm is appropriately modified. This paper discusses several types of modifications of the convergence criteria. Computer simulation shows that the proposed modifications improve the performance of the FC decoding algorithm.