  We calculate the non-forward quark matrix elements of operators with two
covariant derivatives needed for the renormalisation of the second moment of
generalised parton distributions in one-loop lattice perturbation theory using
Wilson fermions. For some representations of the hypercubic group commonly used
in simulations we determine the sets of all possible mixing operators. For
those representations the one-loop mixing matrices of renormalisation factors
are found. Due to non-vanishing contributions of operators with external
ordinary derivatives the number of contributing operators increases compared to
forward matrix elements.
