Optical switching networks (OSN) based on optical directional couplers (DC) may be the most promising candidate to provide a high switching rate when the speed mismatch problem between links (optical fibers) and switches is increasingly serious. Although such switches have many advantages, the DC suffers from an inherent crosstalk problem that can greatly aggravate the switching performance. Based on semi-permutations, a parallel decomposition algorithm,which is called multi-decomposition, is proposed in this paper for solving the optical crosstalk problem in optical multi-log2N switching networks. According to the number of planes in a multi-log2N network, the multi-decomposition is performed in parallel to partition a permutation into several sub-permutations, each of which is established without crosstalk within each plane. We demonstrate that our algorithm can completely remove the crosstalk in optical multi-log2N networks when n is even, and that it may be generated only in the stage (n-1)/2 (i.e., the middle stage) when n is odd, but the corresponding probability of generating crosstalk is to be less than or equal to $\frac{1}{2^{(n+1)/2}-1}$ . In addition, our algorithm can achieve a low complexity for decomposition a permutation due to its parallelism so that any permutations can be realized in multi-log2N networks under the constraint of avoiding crosstalk.