A new version of subnetwork analysis is developed to determine multiple steady states in family members of complex reaction networks. In the analysis, one of its subnetworks admits a zero-eigenvalue steady state and its eigenvector is in the stoichiometric subspace. The new version can be used to determine the capacity of multiple steady states in more general family networks than the old one. Without the simplification of the complex network by the quasi-steady-state manipulation, this method improves the study of a large family of networks, instead of the case-by-case study. These advantages are demonstrated by an enzyme kinetic involving two substrates operating in an isothermal CSTR. The hysteresis and bifurcation diagrams of the studied reaction network are presented. The effects of rate constants on the steady-state multiplicity are discussed.