Additive Runge-Kutta methods for systems of I.V.Ps. x^\prime=f(t, x) , x(t_0)=x_0 have proved useful in many applications. A method of this type is characterized by a pair of methods ( A , B ), where the method A is semi-implicit and A-stable and the method B is explicit. For stiff systems, these methods may be used with a sequence of decompositions f=J^(m)x+g^(m)(t, x) , which is established by taking J ( m ) as approximation to the Jacobian of f at t m and then setting g^(m)(t, x)= f(t, x)-J^(m)x . An additive method with equal non-zero diagonal elements in A gives a computational advantage over many implementation schemes for SIRKs and DIRKs methods, for which the modified Newton or any other iteration method is used. A direct generalization of the algebraic stability is used to obtain some embedded additive R-K methods of order p ≤4 with improved stability properties.