The approach for the integration over a region covered by zero-flux surface is described. This approach based on the surface triangulation technique is efficiently realized in a newly developed program TWOE. The elaborated method is tested on several atomic properties including the source function. TWOE results are compared with those produced by using well-known existing programs. Absolute errors in computed atomic properties are shown to range usually from 10−6 to 10−5 au. The demonstrative examples prove that present realization has perfect convergence of atomic properties with increasing size of angular grid and allows to obtain highly accurate data even in the most difficult cases. It is believed that the developed program can be bridgehead that allows to implement atomic partitioning of any desired molecular property with high accuracy. © 2012 Wiley Periodicals, Inc.