  The existing derivations of a heavy quark effective theory (HQET) are
analyzed beyond the next-to-leading order in $1/m$. With one exception they are
found to be incorrect. The problem is a wrong normalization of the heavy quark
field in the effective theory. We argue that the correct effective theory
should be given by a Foldy--Wouthuysen type field transformation to all orders
in $1/m$. The renormalization of the resulting Lagrangian to order $1/m^2$ is
performed allowing for inclusion of effects arising through vacuum
polarization. Our results for the anomalous dimensions disagree with the
existing ones. Some applications are considered.
