The notion of β-normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost β-normal spaces, which is a simultaneous generalization of βnormal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak β-normality, in terms of θ-closed sets, which turns out to be a simultaneous generalization of β-normality and θ-normality. A space X is said to be weakly β-normal (wβ-normal) if for every pair of disjoint closed sets A and B out of which, one is θ-closed, there exist open sets U and V such that A ∩ U = A, B ∩ V = B and U ∩ V = ∅. It is shown that wβ-normality acts as a tool to provide factorizations of normality.