A single set of coordinates, which is optimal for both asymptotic product and reactant, is difficult to find in a state-to-state reactive scattering calculation using the quantum wave packet method. An interaction-asymptotic region decomposition (IARD) method was proposed in this work to solve this "coordinate problem." In the method, the interaction region and asymptotic regions are applied with the local optimal coordinate system, i.e., hyperspherical and corresponding Jacobi coordinates. The IARD method is capable of efficiently and accurately accomplishing a calculation with a grid box for the Jacobi coordinate R extending several hundred bohrs for both reactant and product arrangements. We demonstrate the effectiveness of the IARD method with the reaction of H + HD, which is the simplest direct reaction, and F + HD, which is a typical reaction involving resonances with products of extremely slow translational energy and requires extremely long absorbing potential in all channels.