With neural networks becoming pervasive in applications where safety matters, verifying their correctness remains a major challenge — particularly at scale. This paper introduces ReCIPH, a heuristic called Relational Coefficients for Input Partitioning Heuristic, designed to accelerate neural network verification. By leveraging linear relaxations and symbolic relations computed during analysis, ReCIPH guides input-space partitioning on dimensions most likely to influence outputs. Experiments on benchmark networks (including the ACAS-Xu suite) and an industrial case demonstrate up to one to two orders of magnitude reduction in the number of subproblems and substantial reductions in verification time — all without extra computational cost. The results show that ReCIPH significantly outperforms naive or gradient-based partitioning heuristics, making formal verification more scalable and practical for low-dimensional inputs.