  The QED renormalization is restudied by using a mass-dependent subtraction
which is performed at a time-like renormalization point. The subtraction
exactly respects necessary physical and mathematical requirements such as the
gauge symmetry, the Lorentz- invariance and the mathematical convergence.
Therefore, the renormalized results derived in the subtraction scheme are
faithful and have no ambiguity. Especially, it is proved that the solution of
the renormalization group equation satisfied by a renormalized wave function,
propagator or vertex can be fixed by applying the renormalization boundary
condition and, thus, an exact S-matrix element can be expressed in the form as
written in the tree diagram approximation provided that the coupling constant
and the fermion mass are replaced by their effective ones. In the one-loop
approximation, the effective coupling constant and the effective fermion mass
obtained by solving their renormalization group equations are given in rigorous
and explicit expressions which are suitable in the whole range of distance and
exhibit physically reasonable asymptotic behaviors.
