  That muon neutrinos $\nu_{\mu}$ oscillating into the mixture of tau neutrinos
$\nu_{\tau}$ and sterile neutrinos $\nu_{s}$ has been studied to explain the
atmospheric $\nu_{\mu}$ disappearance. In this scenario, the effect of Earth
matter is a key to determine the fraction of $\nu_{s}$. Considering that the
Earth matter density has uncertainty and this uncertainty has significant
effects in some neutrino oscillation cases, such as the CP violation in very
long baseline neutrino oscillations and the day-night asymmetry for solar
neutrinos, we study the effects caused by this uncertainty in the above
atmospheric $\nu_{\mu}$ oscillation scenario. We find that this uncertainty
seems to have no significant effects and that the previous fitting results need
not to be modified fortunately.
