We find that the classical failure criteria, i.e., maximum normal stress criterion, Tresca criterion, Mohr-Coulomb criterion, and von Mises criterion, cannot satisfactorily explain the tensile fracture behavior of the bulk metallic glass (BMG) materials. For a better description, we propose an ellipse criterion as a new failure criterion to unify the four classical criteria above and apply it to exemplarily describe the tensile fracture behavior of BMGs as well as a variety of other materials. It is suggested that each of the classical failure criteria can be unified by the present ellipse criterion depending on the difference of the ratio alpha=tau(0)/sigma(0).

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