Let X be a vector space and Y be a Banach space. Our aim in this paper is to investigate the Hyers-Ulam stability problem of the following bi-additive functional equation f(x + y, s − t) + f(x − y, s + t)=2f(x, s) − 2f(y, t), x, y, s, t ∈ X, where f : X × X → Y . As a consequence, we discuss the stability of the considered functional equation in a restricted domain and in the set of Lebesgue measure zero.