Most of the chemical reactions are modelled as initial value problems (IVP) where the derivative can be expressed as a quadratic function of the dependent variable. Some of the variables in these IVPs change rapidly as time progresses, whereas others vary very slowly, indicating the presence of stiffness. Singly Diagonal Implicit Runge–Kutta (SDIRK) pairs possess an interesting alternative for dealing with such problem. Software SDIRK4 applies a five stage pair SDIRK method of accuracy orders 4(3). In this paper by exploiting the presence of quadratic property, we derive a 5(3) order pair SDIRK methods at the same cost. Numerical results over well known chemical kinetics problems justify our effort.