In this paper, our main task is to provide the mathematical characterization for the non‐negativity of a given homogeneous real Weierstrass canonical pencil. Following the work of Uhlig  and Pantelous et al. , we determine analytically the family into a relevant set of indeterminates S, Ŝ. This new approach might be easily transferred into a standard computational routine by using simple Matlab m‐files. A numerical example is also provided.