On rectifying curves in Euclidean 3-space

First, we study rectifying curves via the dilation of unit speed curves on the unit sphere S^2 in the Euclidean space E³. Then we obtain a necessary and sufficient condition for which the centrode d (s) of a unit speed curve (s) in E³ is a rectifying curve to improve a main result of cd05. Finally, we prove that if a unit speed curve (s) in E³ is neither a planar curve nor a helix, then its dilated centrode (s) = (s) d (s), with dilation factor, is always a rectifying curve, where is the radius of curvature of.