Constancy adding space extension is a technique to convert ODE of the form (x) over dot(t) = F-0 + F(1)x(t)+ F(2)x(t)(circle times 2) to form (s) over dot = G(1)s+G(2)P(-1)s(circle times 2). There are arbitrary parameters in the representation. These parameters may be utilized in such a way that G(1) becomes a multiple of identity matrix. Then, using a function transformation it is possible to obtain the form d (s) over tilde (u)/du = G2P(-1)(s) over tilde (u)(circle times 2). Therefore, a new universal representation for ODEs with second degree multinomial right hand side functions is proposed. There are remaining arbitrary parameters of the space extension and this paper also focuses on how to choose them.