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In this paper a general transformation for block- diagonalization (decoupling) of multi time-scale singularly perturbed linear systems composed of N subsystems is introduced. The resulting decoupling is consistent to subsystem time-scales and produces N completely independent subsystems. The block-diagonalization transformation matrix is obtained by successive solutions of reduced-order nonsquare, nonsymmetric, algebraic Riccati equations. The nonsquare, nonsymmetric, algebraic Riccati equations can be efficiently solved by the Newton iterative method.