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The subject matter of this paper is the representation of the solution of the linear differential equation Y′ = AY - YB, Y(O) = Yo, in the form Y(t) = eΩ(t)Yo and the representation of the function Ω as a generalisation of the classical Magnus expansion.An immediate application is a new recursive algorithm for the derivation of the BakerCampbell-Hausdorff formula and its symmetric generalisation.