  This paper presents an extension of the matrix element method to
next-to-leading order in perturbation theory. To accomplish this we have
developed a method to calculate next-to-leading order weights on an
event-by-event basis. This allows for the definition of next-to-leading order
likelihoods in exactly the same fashion as at leading order, thus extending the
matrix element method to next-to-leading order. A welcome by-product of the
method is the straightforward and efficient generation of unweighted
next-to-leading order events. As examples of the application of our
next-to-leading order matrix element method we consider the measurement of the
mass of the Z boson and also the search for the Higgs boson in the four lepton
channel.
