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An approach to generalize any kind of collinear functional in density functional theory to noncollinear functionals is proposed. This approach satisfies the correct collinear limit for any kind of functional, guaranteeing that the exact collinear functional after generalization is still exact for collinear spins. Besides, it has well-defined and numerically stable functional derivatives, a desired feature for noncollinear and spin-flip time-dependent density functional theory. Furthermore, it provides local torque, hinting at its applications in spin dynamics.