Brain-inspired computing is a novel research field involving multiple disciplines, which may have important implications for the development of computational neuroscience, artificial intelligence, and computer architectures. Currently, one of the key problems in this field is that brain-inspired software and hardware are usually tightly coupled. A recent study has proposed the notion of neuromorphic completeness and the corresponding system hierarchy design. This completeness provides a theoretical support for realizing the decoupling of hardware and software of brain-inspired computing systems, and the system hierarchy design can be viewed as a reference implementation of neuromorphic complete software and hardware. As a position paper, this article first discusses several key concepts of neuromorphic completeness and the system hierarchy for brain-inspired computing. Then, as a follow-up work, we propose a design method for software-hardware decoupling hardware design of brain-inspired computing, namely, an iterative optimization process consisting of execution primitive set design and hardware implementation evaluation. Finally, we show the preliminary status of our research on the FPGA based evaluation platform. We believe that this method would contribute to the realization of extensible, neuromorphic complete computation primitive sets and chips, which is beneficial to realize the decoupling of hardware and software in the field of brain-inspired computing systems.