  We present a systematic procedure to obtain the one-loop low-energy effective
Lagrangian resulting from integrating out the heavy fields of a given
ultraviolet theory. We show that the matching coefficients are determined
entirely by the hard region of the functional determinant involving the heavy
fields. This represents an important simplification with respect the
conventional matching approach, where the full and effective theory
contributions have to be computed separately and a cancellation of the infrared
divergent parts has to take place. We illustrate the method with a descriptive
toy model and with an extension of the Standard Model with a heavy real scalar
triplet. A comparison with other schemes that have been put forward recently is
also provided.
