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The paper presents an improvement of the weighted bit-flipping (WBF) decoding algorithm for LDPC codes proposed by Liu and Pados (2003). Simulation results show that the improved WBF algorithm provides about 0.25 dB coding gain over the Liu-Pados WBF algorithm. Also included in the paper is a simplified loop-detection algorithm, which is much easier to implement than the one proposed by Liu and Pados. The proposed WBF algorithm is particularly effective for decoding LDPC codes whose parity check matrices have large row/column weights such as finite geometry LDPC codes.