In Egypt , members of the Greek Orthodox Patriarchate were also known as Melkite , because they remained in communion with the Ecumenical Patriarch of Constantinople after the schism that followed the Council of Chalcedon in 451 . Members of the church were once known as Melkites , because they remained in communion with the Ecumenical Patriarchate of Constantinople after the schism that followed the Council of Chalcedon in 451 .