A new formulation is proposed for obtaining the SCF wave functions. It is based on an exponential transformation of spin-orbitals which obviates the use of Lagrangian multipliers. A general method is developed for determining explicit expressions for the successive derivatives of the energy with respect to the new variables. The total energy and the wave function are obtained by an iterative procedure, the convergence of which is shown to be quadratic. The method itself provides information as to the Hartree-Fock stability - or instability - of the SCF solution. The method of exponential transformation of molecular orbitals is applicable to closed-shell systems, as well as to a large variety of open-shell systems. As an illustration of the procedure the results of ab initio calculations for ammonia, methane, formaldehyde, and aziridine are given. © 1980 American Institute of Physics.