A self-consistent pseudopotential technique based on the density functional formalism is used for calculating the electronic structure and total energy of an unsupported monolayer of aluminum in the  orientation. The results are presented for a number of values of the lattice constant and the equilibrium value is determined by an energy minimization criterion. One significant result of our study is that the lattice constant in a monolayer is contracted by about 10% with respect to the bulk lattice constant. This result is similar to the one recently reported by Wimmer for the two-dimensional Cs layer. Another conclusion is that the total bandwidth for the relaxed monolayer is about 1.5 eV larger than the value for the bulk truncated monolayer. The cohesive energy is increased by about 0.3 eV per atom upon relaxation. These findings are important in the study of thin-film deposition on substrates and in the molecular beam epitaxy. Another area for which our work has implications has to do with the electronic structure of a Cu(001) monolayer. © 1985, American Vacuum Society. All rights reserved.