  A focal representation of a generic regular curve {\gamma} in E^{m+1}
consists of the centers of the osculating hyperplanes. A k-slant helix {\gamma}
in E^{m+1} is a (generic) regular curve whose unit normal vector V_{k} makes a
constant angle with a fixed direction U in E^{m+1}. In the present paper we
proved that if {\gamma} is a k-slant helix in E^{m+1}, then the focal
representation C_{{\gamma}} of {\gamma} in E^{m+1} is a (m-k+2)-slant helix in
E^{m+1}.
