In this paper, we study the central configuration of the Rhomboidal five-body problems. Four of the masses are placed at the vertices of the Rhombus and the fifth body is placed at the centre of mass of the system. A central configuration for n-body problem is formed if the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration. We identify regions in the phase space where it is possible to chose positive masses which will make the configuration central. We also show that in the compliment of those regions no central configurations are possible. © 2012 American Institute of Physics.