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In this paper, we give some properties of the bi-Jensen functional equation \[4f\left(\frac{x+y}{2}, \frac{z+w}{2}\right)=f(x,z)+ f(x,w)+ f(y,z)+ f(y,w)\] and the Hyers-Ulam stability is investigated. Also, we establish the Hyers-Ulam stability of the bi-Jensen functional equation on some restricted domains. Finally, we apply the obtained results to study some of interesting asymptotic behaviors of bi-Jensen functions.