Of the various methods of improving the Onsager theory of geminate electron-ion recombination for arbitrary mean free path, an especially promising one involves the use of the Metropolis rejection criterion [A. Mozumder, Radiat. Phys. Chem. 72 (2005) 73; 74 (2005) 227]. The present Letter further includes the effect of finite reaction probability at the reaction radius by a tridiagonal matrix method. Model calculations suggest usefulness when the overall mobility exceeds similar to 1 cm(2) V (1) s (1). Variations of the escape probability with mean free path, initial separation and final reaction rate are discussed. (C) 2011 Elsevier B.V. All rights reserved.