Yes, but the "Orthodox" understanding of the matter is a novelty constructed after the fact, to avoid what was known always and everywhere that the Greek Church and Constantinople is entirely subject to the Apostolic See of Rome.
Here is one the of great Greek Fathers of the Church in the seventh century, a champion of orthodoxy, always Catholic and always Roman, St.Maximus the confessor, explain the matter with a typical profundity, showing that the prerogatives of Rome as foundation of the universal Church are by divine institution and that the very divine promise precludes precisely the false claim of the Greeks.
How much more in the case of the clergy and Church of the Romans, which from of old until now, as the elder of all the Churches under the sun, presides over all? Having surely received this canonically, as well from councils and the Apostles, as from the princes of the latter, and being numbered in their company, she is subject to no writings or issues of synodical docuмents, on account of the eminence of her pontificate, even as in all these things all are equally subject to her according to sacerdotal law.
The extremities of the earth, and all in every part of it who purely and rightly confess the Lord look directly towards the most holy Roman Church and its confession and faith, as it were to a sun of unfailing light, awaiting from it the bright radiance of the sacred dogmas of our Fathers according to what the six inspired and holy councils have purely and piously decreed, declaring most expressly the symbol of faith.
For from the coming down of the incarnate Word amongst us, all the Churches in every part of the world have held that greatest Church alone as their base and foundation, seeing that according to the promise of Christ our Saviour, the gates of hell do never prevail against it, that it has the keys of a right confession and faith in Him, that it opens the true and only religion to such as approach with piety, and shuts up and locks every heretical mouth that speaks injustice against the Most High.
The Apostolic see, which from the incarnate Son of God Himself, and also by all holy synods, according to the holy canons and definitions, has received universal and supreme dominion, authority and power of binding and loosing over all the holy Churches of God which are in the whole world — for with it the Word who is above the celestial powers binds and looses in heaven also.
For his tireless defense of Roman orthodoxy, he was asked in spite, "Why do you love the Romans and hate the Greeks? He said, "I love the Greeks, we share the same language; but the Romans, we share the same faith". Then they cut out his tongue and put him to death. Today, even the separated Greeks venerate him as a Father of the Church. He is a perfect example of truth lived out in charity, full of knowledge and wisdom and full of sanctity and holiness as befits the Saints of God.