An analytical five-term expansion potential is suggested to improve the recently proposed energy consistent method (ECM) potential based on a three-term expansion [Weiguo Sun, Mol. Phys. 92, 105 (1997) and Weiguo Sun and Hao Feng, J. Phys. B: At., Mol. Opt. Phys. 32, 5109 (1999)]. Applications of the new ECM to the electronic excited state 31Ⅱ of NaK, the excited state 23Σ+g of Na2, and the excited states 31Σ+u 1 and 31Ⅱu of K2 molecules show that the new ECM potential not only agrees excellently with the known Rydberg-Klein-Rees (RKR) data or accurate configuration interaction (CI) studies but also gives the potential data at the molecular asymptote and the dissociation region where experimental and quantum mechanical studies may have difficulties. The new ECM can correct the artifact which appeared in the three-term expansion potentials of both the previous ECM and the Huxley-Murrell-Sorbie (HMS) potential and can describe some states to which both the previous ECM and the HMS fail.