G. Saban studied on Darboux curves and obtained some results on a surface in E 3 [1 ]. E. Özdamar and H. Hacısalihoğlu evaluated the çenter of (n-l)-osculating sphere at ct (t) of a curve a in En [2J. In this paper we defined general Darboux curve on a hypersufrace M in En . Then we generalized some results of G. Saban by using [2],