What a lot of people would consider an old Roman Catholic way of worshipping predates Roman Catholicism, which began in about AD 1054. This way of worshipping is actually an ancient Orthodox way of worshipping in the Western world. Western Rite worship looks more Anglican or Roman Catholic than the Eastern Rite, but the Western Rite is Orthodox.
If you're curious about the Western Rite of the Orthodox Church, I recommend that you watch the brief video about St. Paul Orthodox Church in Houston, TX.
You may also read an article I wrote last summer on "Ancient Spirituality in the British Isles."