  Solar and atmospheric neutrino oscillations are consistent with a
tribimaximal form of the mixing matrix $U$ of the lepton sector. Exact
tribimaximal mixing leads to $\theta_{13}=0$. Recent results from the Daya Bay
and RENO experiments have established a non-zero value of $\theta_{13}$.
Keeping the leading behaviour of $U$ as tribimaximal we perform a
model-independent perturbative calculation to incorporate a non-vanishing
$\theta_{13}$. We identify the nature of the perturbation matrix and consider
the possibility of the solar neutrino splitting also resulting from it. We
calculate up to first order in perturbation theory and evaluate the deviations
proportional to $\sin \theta_{13}$ while including CP-nonconservation. Finally,
we briefly discuss a gauge model where such an addition to the neutrino mass
matrix arises through one-loop effects.
