  The conjecture of the existence and the uniqueness of the strictly convex
quadrilateral central configuration for the Newtonian 4-body problem is one of
the most-talked open problems in the study of the classical n-body problems in
celestial mechanics. MacMillan and Bartky first gave its general existence in
the 1930s and a particular case for its uniqueness. Still, the general case has
yet to be solved perfectly since it was considered by Sim'{o} and Yoccoz in the
1980s and was first mentioned by Albouy and Fu in 2008 in the formal
publication. Using coordinates of mutual distances and Morse's critical point
theory, we give the (at most) uniqueness of the planar strictly convex 4-body
central configuration when the angle of one pair of the opposite sides is
given.
