  Since fields in the heavy quark effective theory are described by both a
velocity and a residual momentum, there is redundancy in the theory: small
shifts in velocity may be absorbed into a redefinition of the residual
momentum. We demonstrate that this trivial reparameterisation invariance has
non-trivial consequences: it relates coefficients of terms of different orders
in the $1/m$ expansion and requires linear combinations of these operators to
be multiplicatively renormalised. For example, the operator $-D^2/2m$ in the
effective lagrangian has zero anomalous dimension, coefficient one, and does
not receive any non-perturbative contributions from matching conditions. We
also demonstrate that this invariance severely restricts the forms of operators
which may appear in chiral lagrangians for heavy particles.
