The purpose of present study was to clarify the rule system for the transformation-operations of coordinate system between the child's own viewpoint and the other's one in spatial representation tasks with forming the action of projection (AP). Based on performance levels of the projection test for first-grade children (6:09), six pairs of matched subjects who had not yet acquired AP were selected among 34 children. The training program of five steps consisted of the following three subordinate operations which were assumed to underlie AP; identification of the origin, setting of the X-Y axes, and transformation of the coordinates (X, Y) between viewpoints. Main results were as follows: (1) The training program raised the level of AP from low to high. (2) Through analysis of transformation-patterns, the rule system illustrated Fig. 4 which was constructed with three factors; transformation of the axis, reversal of the axis, and degree of persistence of the child's own view was identified. (3) The acquired transformation ability improved highly the performance of Piaget's “three mountains task”.