The optimal s-stage second order explicit SSP Runge-Kutta method has SSP coefficient s-1 and Shu-Osher form $$\begin{eqnarray} \beta_{i,i-1} & = \left\{ \begin{array}{ll} \frac{1}{s-1} & 1\le i\le s-1 \\ \frac{1}{s} & i=s \end{array}\right. \\ \alpha_{i,i-1} & = \left\{ \begin{array}{ll} 1 & 1\le i\le s-1 \\ \frac{s-1}{s} & i=s \end{array}\right. \\ \alpha_{s,0} & = \frac{1}{s}. \end{eqnarray} $$