The second bound state of the biexcitons in a quantum dot, with orbital angular momentum L = 1, is reported. By using the method of few-body physics, the binding energy spectra of the second bound state of a biexciton in a GaAs quantum dot with a parabolic confinement have been calculated as a function of the electron-to-hole mass ratio and the quantum dot size. The fact that the biexcitons have a second bound state may aid in the better understanding of their binding mechanism.