  Assuming only the non-zero electron and tau neutrino components
$\epsilon_{ee}$, $\epsilon_{e\tau}$, $\epsilon_{\tau\tau}$ of the non-standard
matter effect and postulating the atmospheric neutrino constraint
$\epsilon_{\tau\tau}=|\epsilon_{e\tau}|^2/(1+\epsilon_{ee})$, we study the
sensitivity to the non-standard interaction in neutrino propagation of the T2KK
neutrino long-baseline experiment. It is shown that T2KK can constrain the
parameters $|\epsilon_{ee}|\lesssim 1$, $|\epsilon_{e\tau}|\lesssim 0.2$. It is
also shown that if $|\epsilon_{e\tau}|$ and $\theta_{13}$ are large, then T2KK
can determine the Dirac phase and the phase of $\epsilon_{e\tau}$ separately,
due to the information at the two baselines. We also provide an argument that
the components $|\epsilon_{\alpha\mu}|$ $(\alpha=e,\mu,\tau)$ must be small for
the disappearance oscillation probability to be consistent with high-energy
atmospheric neutrino data, which justifies our premise that these quantities
are negligible.
