The polyesters made from the condensation of isophthalic acid (IA) or terephthalic acid (TA) with the mesogenic diol 4,4’-bis (6-hydroxy hexoxy)biphenyl (BHHBP) are both reported to show a smectic mesophase. However, in our previous work, we found evidence for a mesophase in the polyester containing BHHBP and IA, but not in the one with BHHBP and TA. For the BHHBP-IA polyester, we thought the phase sequence on cooling was I --> S-A --> K, while on heating the situation was unresolved; there was some indication that on heating, a K --> I transition occurs without any intervening mesophase. In other words, it was suspected that the mesophase in the IA polyester was monotropic. In this work, we have now obtained firm evidence that the mesophase behavior of the BHHBP-IA polyester is indeed monotropic. Further, an additional complexity has been found : on cooling, there is in fact a nematic phase, besides a smectic A, and a crystal phase. However, the mesophase appears to be complex. As the nematic and smectic textures occurred simultaneously, it seems that the mesophase is a nematic-smectic biphase.