The motion of triple stellar systems whose components are at rest at the initial epoch is studied. In this study all the components have equal masses, and at the initial epoch the component A is at (-1/2, 0) on the (x, y)-plane, B is at (1/2, 0), and C is anywhere in the region (s) bounded by the positive x-axis, y-axis and a line expressed by (x+1/2)2 + + y2 = 1. By this way all the possible initial configurations are given.