In order to enhance the intrinsic robustness or prolong the disentangling time of entangled states, the influence of qubi-basis on the robustness of two-qubit entanglement under local amplitude-damping environments is discussed. The decay law and lifetime of entanglement under various qubit-bases are displayed. The optimal qubit-bases in variety of cases are found. When an entangled state is prepared in an optimal qubit-basis, the entanglement decays most slowly and won't disappear in a finite time. The results imply that one could improve the ...