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 robustness of entangled states by rotating the bases of qubits， which are expected to be helpful for increasing the qualities or efficiencies of entanglement-based quantum protocols.