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The Great Schism, also known as the Great Schism of 1054 or the East-West Schism was the schism by which the Roman Catholic Church and the Eastern Orthodox Church separated. Cultural and liturgical differences were debated as early as the 6th century; they officially split by excommunicating each other in 1054, and only ended the mutual anathema in 1965.
 Official reasons for the separation
The official disagreements between the two churches were numerous and included seemingly trivial issues like baking and more critical issues of the nature of the Holy Spirit. For example, the Roman Catholic church insisted (without biblical evidence) that the Eucharist must be unleavened bread. The Eastern Orthodox Church accepted the use of leavened bread. There was also the more esoteric question of whether the Holy Spirit proceeds from the Father or from the Father and the Son - something known as the Filioque.
Of course, like most things, "official positions" are rarely as important as power and politics.
Muslim conquests had reduced the Catholic territory, leaving only two (Constantinople and Rome) of the five sees (Alexander, Antioch and Jerusalem had fallen). Bishop of Rome, Pope Leo IX, thought he should be head of the remaining Catholic Body. The Patriarch of Constantinople, Michael Cerularius thought otherwise.