The Byzantine Rite

Fr John Hardon defines it in his Modern Catholic Dictionary as, BYZANTINE RITE. Ritual and ecclesiastical policy followed by the Church of Constantinople. The second most widely used rite after the Roman, it has three forms: 1. the Liturgy of St. James the Elder, modified by St. Basil and named after him; 2. St. John Chrysostom's later modification, which became the common Eucharistic service of Constantinople. Though it did not displace the original St. Basil's, it did limit its use; 3. the liturgy of the Presanctified, essentially the distribution of the Blessed Sacrament consecrated on the preceding Sunday.

Also known as the Greek Rite or the Rite of Constantinople, the name identifies the wide range of cultural, liturgical, and canonical practices that developed in the  Church of Constantinople.

The Catholic Churches which use the Byzantine Rite are:

• Albanian Greek Catholic Church
• Belarusian Greek Catholic Church
• Bulgarian Greek Catholic Church
• Byzantine Catholic Church of Croatia and Serbia
• Greek Byzantine Catholic Church
• Melkite Greek Catholic Church
• Hungarian Greek Catholic Church
• Italo-Albanian Catholic Church
• Macedonian Greek Catholic Church
• Romanian Church United with Rome, Greek-Catholic
• Russian Greek Catholic Church
• Ruthenian Greek Catholic Church
• Slovak Greek Catholic Church
• Ukrainian Greek Catholic Church

On a personal note, having converted from the Orthodox Church of Serbia, I am juridically a member of the Byzantine Catholic Church of Croatia and Serbia.