However we Orthodox would not say we are a branch. The Orthodox Church is the original Church in its fullness preserving all that the Apostles taught us unaltered. Other Christianities have fallen away from orthodoxy (such as Rome in 1054), but Orthodoxy remains, like Christ Jesus, the same yesterday today and tomorrow forever.
Please forgive me if I have unintentionally offended any non-Orthodox believers out there, but for us, Orthodoxy is like the precious jewel that was buried in the field, that one sold all they had to possess - it (Orthodoxy) is the pearl of great price.