calculations with the Riemann curvature

Question

I was doing a calculation with the Riemann tensor and in a part of that calculation I got these terms $+\frac{\alpha}{4}R_{ijl}^qRm^2_{kq}-\frac{\alpha}{2}R_{ijk}^qRm^2_{ql}$ where $Rm^2$ is the $(2,0)$-tensor given by $Rm_{ij}^2:=R_{iklm}R_j^{klm}$. I´m not so familiar with de $*-$notation. Is it correct if I write those terms as $Rm*Rm^2$?. Where could I get information about the rules of $*-$notation? Thanks!