Some research institutions have developed biped-walking robots aimed for prospective cooperative working with humans. Among various research items related to them, waist joint is important because it gives so much influence to the stability of upper body. Many biped-walking robots developed so far use a single rotary joint in waist joint, but it has a crucial drawback in energy consumption to stabilize the upper body. In our research a new mechanism has proposed, which consists of a crossover 4-bar linkage controlled by two motors via springs. The crossover 4-bar linkage is intrinsically more stable than a single rotary joint. Two springs are arranged counteractively to regulate the stiffness of the waist joint. This paper shows a stability index to evaluate stability of the crossover 4-bar linkages. It also proposes a mechanism of the waist joint followed by examinations of allocation of the linkages and springs in terms of stiffness control. We developed a test machine based on the simulation results and achieved some experiments, which clearly showed the experimental results are well coincident with the theoretical one.