  The critical exponents $\nu_{L2}, \eta_{L2}$ and $\gamma_{L2}$ of a uniaxial
Lifshitz point are calculated at two-loop level using renormalization group and
$\epsilon_{L}$-expansion techniques. We found a new constraint involving the
loop momenta along the competition axis, which allows to solve the two-loop
integrals. The exponent $\gamma_{L2}$ obtained using our method is in good
agreement with numerical estimates based on Monte Carlo simulations.
