In contact-rich tasks, setting the stiffness of the control system is a critical factor in its performance. Although the setting range can be extended by making the stiffness matrix asymmetric, its stability has not been proven. This study focuses on the stability of compliance control in a robot arm that deals with an asymmetric stiffness matrix. It discusses the convergence stability of the admittance control. The paper explains how to derive an asymmetric stiffness matrix and how to incorporate it into the admittance model. The authors also present simulation and experimental results that demonstrate the effectiveness of their proposed method.