The schedulability analysis for fixed-priority pre-emptive scheduling (FPPS) plays a significant role in the real-time systems domain. The so-called Hyperplanes Exact Test (HET) is an example of an exact schedulability test for FPPS. In this paper, we aim at improving the efficiency of HET by combining it with initial values for exact response time analysis (RTA). We call the resulting improved test HETI and show by means of simulations that HETI is more efficient than HET.