The Modified Embedded Atom Method (MEAM) is applied to dimers of several materials whose parameters are published by Baskes. For some materials, the MEAM is found to return fatal errors which never arises in bulk systems. The problem of the fatal error is found to be because of a formalism which calculates the background electron density, and the usage of an original formalism is found to prevent the problem. Since the dimer is the most non-bulk system, this problem has to be considered in the application of MEAM to non-bulk systems. The MEAM calculation has been retried for all of the dimers by using the original formalism. The results by the MEAM are compared with density functional theory (DFT) calculations. The usage of the original formalism returns the consistent results for most of the dimers. This suggests that the original formalism has to be used for the background electron density calculation, if the MEAM would be applied to non-bulk systems. It would also suggest that the MEAM parameters should be modified for some materials (Mo, Cr, C).