The alternate direction method of multipliers (ADMM) approach has been recently considered for LDPC decoding. It has been approved to enhance the error rate performance compared with conventional message passing (MP) techniques in both the waterfall and error floor regions at the cost of a higher computation complexity. In this letter, a formulation of the ADMM decoding algorithm with modified computation scheduling is proposed. It increases the error correction performance of the decoding algorithm and reduces the average computation complexity of the decoding process thanks to a faster convergence. Simulation results show that this modified scheduling speeds up the decoding procedure with regards to the ADMM initial formulation while enhancing the error correction performance. This decoding speed-up is further improved when the proposed scheduling is teamed with a recent complexity reduction method detailed in [1] (Wei et al. IEEE Communications Letters 2015).