Did Byzantium and Latin West ever had friendly relations?

The more I read about History of Middle Ages, it seemed like both the Byzantium and Latin West always seemed to disdained one another to a large degree. Constantinople always attempt to assert sovereignty over the traditional lands of Western Roman Empire such as their attempts to claim Italian peninsula fighting the Lombards from 568-750 and later the Italian Normans from 1080-1186.

The Western Crusaders were hired by the Byzantines since First, Second and Third Crusades but it seemed like during the whole time, the Crusaders went to establish their own kingdoms and by Fourth Crusade, the Crusaders decided to sack Constantinople in 1204.

From all this was there any serious rapproachment between Latin West and Byzantine Empire?