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We study the stability property of a simple periodic solution of an autonomous neutral functional differential equation (NFDE) of the form $${d\over dt} D(x_t) = f (x_t).$$ A new proof based on local integral manifold theory and the implicit function theorem is given for the classical result that a simple periodic orbit of the equation above is asymptotically orbitally stable with asymptotic phase. The technique used overcomes the difficulty that the solution operator of a NFDE does not smooth as $t$ increases.