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In order to avoid linear dependencies of localized orbitals, the present localization methods either constrain orbital transformations to be unitary, that is, metric preserving, or, when it comes to variable-metric methods, fix the facilities of non-orthogonal localized orbitals. Right here, we developed a unique method to orbital localization, in which these constraints are changed with a single constraint that specifies the utmost allowed deviation through the orthogonality for th