We present results of ab initio calculations of the (H2O)(4)/(H2O)(4)(-) system. The main conclusions of this work are as follows : The calculated results predict that water tetramer anions are metastable systems in agreement with weak spectral manifestation of these systems in gas-phase experiments of Bowen and co-workers; the excess electrons in all four structural isomers of water tetramer anions found in the calculations are attached to the clusters by the virtue of dipole-electron interaction; all four (H2O)(4)(-) anions found in the calculations are almost isoenergetic but have different vertical electron detachment energies (VDEs) ranging from 22 to 279 meV; the most stable cyclic structure of (H2O)(4) has a null dipole moment and does not form a dipole-bound state with an excess electron; the water tetramer anions observed experimentally probably are formed as a result of hydration of the water dimer anion, (H2O)(2)(-), by a neutral water dimer or by hydration of the water trimer anion, (H2O)(3)(-), by a single water molecule; based on calculations, we predict some specific IR vibrational features for the anions which can be used for identification of these species; vibrational analysis of all four anions found in the calculations indicate that they correspond to minima on the potential-energy surface.