Combinatorial testing has been an active research area in recent years. One challenge in this area is dealing with the combinatorial explosion problem, which typically requires a very expensive computational process to find a good test set that covers all the combinations for a given interaction strength (t). Parallelization can be an effective approach to manage this computational cost, that is, by taking advantage of the recent advancement of multicore architectures. In line with such alluring prospects, this paper presents a new deterministic strategy, called multicore modified input parameter order (MC-MIPOG) based on an earlier strategy, input parameter order generalized (IPOG). Unlike its predecessor strategy, MC-MIPOG adopts a novel approach by removing control and data dependency to permit the harnessing of multicore systems. Experiments are undertaken to demonstrate speedup gain and to compare the proposed strategy with other strategies, including IPOG. The overall results demonstrate that MC-MIPOG outperforms most existing strategies (IPOG, IPOF, IPOF2, IPOG-D, ITCH, TConfig, Jenny, and TVG) in terms of test size within acceptable execution time. Unlike most strategies, MC-MIPOG is also capable of supporting high interaction strengths of t > 6.