A practical scheme for the calculation of excited states of the same symmetry as a given reference state is outlined in the context of the Hartree-Fock method. In order to prevent the excited state from "collapsing" into a lower-lying state, the prediagonalized Fock matrix is diagonalized in a restricted subspace, deleting the component associated with the orbital which participates in the excitation. Computationally, the deletion is accomplished by means of a "big shift" of the associated diagonal element of the prediagonalized Fock matrix. The resulting wave function will not be fully relaxed, but can be shown to be orthogonal to the reference state. The method has been implemented in a molecular UHF program. Applications to the 4u;' hole state of CO and to an excited state of the CuCIi-ion are reported.