  We discuss the accurate determination of matrix elements < f| h_w | i > where
neither |i> nor |f> is the vacuum state and h_w is some operator. Using
solutions of the Generalized Eigenvalue Problem (GEVP) we construct estimators
for matrix elements which converge rapidly as a function of the Euclidean time
separations involved. |i> and |f> may be either the ground state in a given
hadron channel or an excited state. Apart from a model calculation, the
estimators are demonstrated to work well for the computation of the B*B
pi-coupling in the quenched approximation. They are also compared to a standard
ratio as well as to the "summed ratio method" of [1,2,3]. In the model, we also
illustrate the ordinary use of the GEVP for energy levels.
