S. Tachibana [10] has defined a confornal Killing tensor in a n-dimensional Riemannian manifold M by a skew symmetric tensor $u_[ji}$ satisfying the equation $$ abla_k u_{ji} + abla_j u_{ki} = 2 ho_i g_{kj} - ho_j g_{ki} - ho_k g_{ji}, $$ where $g_{ji}$ is the metric tensor of M, $ abla$ denotes the covariant derivative with respect to $g_{ji}$ and $ ho_i$ is a associated covector field of $u_{ji}$. In here, a covector field means a 1-form.