The rate constant of the diffusion-controlled recombination of ions has been calculated for large (infinite) ensembles of nonseparable ion pairs. The computer codes have been constructed that simulate diffusion-controlled recombination of ions in model supersaturated solutions with different concentrations of ionic solutes and different dielectric constant of the solution. The simulation runs were performed for C equals 10-4 M, 10-3 M, 10-2 M, 10-1 M and 1 M and, independently, for a wide range of the dielectric constant, from epsilon equals 2 (nonpolar solvent) to epsilon equals 80 (aqueous solutions). The simulations yielded the ion survival probability as a function of time and allowed us to calculate the rate constant of the ion recombination as a function of the ion concentration. The calculated rates are compared with the theoretical Debye-Smoluchowski-type rate constant derived for isolated ion pairs and the Smoluchowski rate constant for neutral reactants. It appears, surprisingly, that the rate constant does not decrease with the increase of concentration (from the kDS value to the Smoluchowski k value, as expected), even in the range of 1 M solutions. The rate constants, for a wide range of the dielectric permittivity, are slightly higher (by about 10 - 20%) than the kDS rate constant and much higher, even by a factor of a hundred in nonpolar solutions, than the Smoluchowski rates.