We investigate the issue of coordinate redefinition invariance by care
fully performing non-linear transformations in the discretized quantum
mechanical path integral, By resorting to hamiltonian path integral m
ethods, we provide the first complete derivation of the extra term (be
yond the usual jacobian term) which arises in the action when a non-li
near transformation is made, We comment on possible connections with t
he renormalization group, by showing that these extra terms may emerge
from a ''blocking'' procedure.