We introduce a finite volume scheme to approximate the one dimensional breakage equations. An interesting feature is that it is simple in mathematical formulation and predicts particle number density and its moments with improved accuracy. Efficiency of the new scheme is compared with the existing finite volume scheme proposed by Bourgade and Filbet (2008) over some test problems. It is seen that the new scheme preserves the volume conservative property of the previous scheme and additionally gives an improved estimation of the particle number density and its zero-order moment. Furthermore, the new scheme is computationally more efficient than the existing one. A detailed mathematical analysis including convergence and consistency of the new scheme is also performed. This analysis proves that the new scheme follows a second order convergence rate irrespective of the nature of the meshes. Several example problems are solved numerically to validate the results. (C) 2016 Elsevier Ltd. All rights reserved.