In this paper we reexamine the stability of the dimer of the ammonium radical NH4 reported recently by Boldyrev and Simons (J. Phys. Chem. 1992, 96, 8840). More flexible diffuse basis sets are introduced designed to give a better representation of the important 3s orbital on N, overlap from which leads to the weak Rydberg bond. At the MP2(full) level of calculation the energetic results, molecular geometry, and vibrational frequencies are generally in good agreement with Boldyrev and Simons, except for the very low-frequency modes. However, the essentially free rotation of the NH4 monomer within the weak Rydberg two-electron bond requires further analysis of the dimer stability. Following a reaction coordinate toward the (strongly exothermic) ground state products 2NH3 + H2 shows that there is a very low barrier of about 2.0 kcal/mol, which disappears when corrected for zero-point energy differences. This will destabilize the dimer and make its observation improbable.