The demonstrated transferability of functional groups defined as proper open systems within the theory of atoms in molecules is used to iteratively construct a one-electron density matrix P and its derived electron density distribution. The initial guess at the density used in the fitting procedure is obtained from the addition of the density distributions of groups defined in parent molecules by the maximal matching of their interatomic surfaces. The method thus takes advantage of the observation that the "zero-flux" boundary condition defining a proper open system maximizes the transferability of the density distribution of a given group between molecules, one that is accompanied by a paralleling transferability in all of its properties. The construction is subject to the constraints that P be idempotent and normalized. The method is applied to the construction of P for the molecules HCH2\CH2X, with X=CH3, NH2, OH, and F, where the vertical bar denotes the new C-C interatomic surface, the new zero-flux boundary. The densities for the groups HCH2\ and \CH2X are defined in their dimer molecules, HCH2\CH2H and XCH2\CH2X.