With a proper combination of compliant joint and position- controlled joint, a link system changes its posture with keeping contact between link system and environment. This is so-called Self-Posture Changing Motion (SPCM) and conveniently used to detect a contact point between robot and unknown object. In conventional approach, a contact point has been computed as an intersecting point between two different link postures before and after SPCM. In general, this computation scheme gives us a contact point with unsatisfactory approximation, while it furnishes us with an exact contact point for a sharp-edged object. In this paper, we first introduces a concept of degree-of-approximation, which is defined as the distance between a computed point and the nearest point over the object surface, and then propers the Neighboring Degree-Of Approximation Equating Method which improves the degree-of-approximation drastically and provides exact contact points not only for a sharp· edged object but also for a constant curved object. Mathematical framework is provided for the proposed computation scheme. Finally, the effectiveness of the proposed scheme is verified by simulations.