The optimal $s^2$-stage third order explicit SSP Runge-Kutta method has SSP coefficient $s^2-s$ and Shu-Osher form $$\begin{eqnarray} \alpha_{i,i-1} & = & \left\{\begin{array}{cc} \frac{n-1}{2n-1} & i=\frac{n(n+1)}{2} \\ 1 & \mbox{otherwise} \\ \end{array}\right. \\ \alpha_{\frac{n(n+1)}{2},\frac{(n-1)(n-2)}{2}} & = & \frac{n}{2n-1} \\ \beta_{i,i-1} & = & \frac{\alpha_{i,i-1}}{n^2-n}. \end{eqnarray}$$ The abscissas of the method are $$\begin{eqnarray} c_i & = & \frac{i-1}{n^2-n}, & \mbox{for } 1 \le i \le (n+2)(n-1)/2 \\ c_i & = & \frac{i-n-1}{n^2-n} &\mbox{for } (n+2)(n+1)/2 \le i \le n^2. \end{eqnarray}$$