Initial state-selected and energy-resolved reaction probabilities, integral cross sections(ICSs), and thermal rate constants of the \textH(^2\textS)+S\textiH(\textX^2\Pi; \nu = 0\text ,j = 0)\to \textSi(^1\textD)+\textH_2(\textX^1 \Sigma_g^+) reaction are calculated within the coupled state(CS) approximation and accurate calculation with full Coriolis coupling(CC) by a time-dependent wave packet propagation method (Chebyshev wave packet method). Therefore, a new ab initio global potential energy surface (PES) of the electronic ground state (1¹A′) of the system, which was recently reported by Li et al. Phys. Chem. Chem. Phys. 2022 24 7759, is employed. The contributions of all partial waves to the total angular momentum J = 80 for CS approximation and J = 90 for CC calculation are considered to obtain the converged ICSs in a collision energy range of 1.0 ×10^–3－1.0 eV. The calculated probabilities and ICSs display a decreasing trend with the increase of the collision energy and show an oscillatory structure due to the SiH₂ well on the reaction path. The neglect of CC effect will lead to underestimation of the ICS and the rate constant due to the formation of an SiH₂ complex supported by the stationary points of the SiH₂(1¹A′) PES. In addition, the results of the exact calculation including CC effect are compared with those calculated in the CS approximation. For the reaction probability, CC and CS calculations change with similar tends, shown by their observations at small total angular momentum J = 10, 20 and 30, and the CC results are larger than the CS results almost in the whole considered energy range at large total angular momentum J = 40, 50, 60 and 70. The gap between CS and CC probability get more pronounced with increasing of J, which reveals that Coriolis coupling effects become more and more important with J increasing for the title reaction. Moreover, the exact quantum-wave calculations show that the thermal rate constant between 300 K and 1000 K for the title reaction shows a similar temperature independent behavior to that for the H + CH reaction, but the value of the rate constant for the H + SiH reaction is an order of magnitude larger than that for the H + CH reaction.