This paper describes a stable knee-stretched walking of a humanoid by the resolved viscoelasticity control (RVC). The RVC method resolves multiple viscoelasticities in task-space, including the center of mass viscoelasticity for balancing, into joint-space viscoelasticity. Although a robust and compliant motion was achieved by the RVC method in previous studies, the conventional knee-bent posture to avoid the kinematic singularity suffered large knee joint torque. In this study, we propose an extension of the RVC capable of the kinematic singularity. We demonstrate through simulations and experiments that the RVC method considering the singularity achieves a stable and human-like walking, reducing the knee joint torque and improving the energy efficiency.