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Whether or not a baptism is performed depends on the bishop and the jurisdiction. My church, the Serbian Orthodox Church, baptizes all converts, regardless of previous baptisms. Most others are much more flexible.
An important point of distinction needs to be made. We only acknowledge one baptism for the remission of sins, and as such the Orthodox Church does not 'recognize' the validity of other baptisms outside of herself; outside of the Church. Those Orthodox churches which do not baptize converts who were previously baptized outside of the Church do this by divine economy.
Basically, when the convert is chrismated into the Church, the seal of the Holy Spirit gives grace to the previous baptism and fulfills it. There is no acknowledgment of sacramental grace outside of the Church. God can give grace however he wants to, the Orthodox Church doesn't dispute that, however we can only affirm that grace which is conferred within the visible parameters of the Church Militant.
Most jurisdictions will accept it if it was performed with the correct Trinitarian formula (by triple immersion in the Name of the Father, Son and Holy Spirit).
I knew the baptism had to be Trinitarian, but I think that divine economy is still applied to those baptisms which were a single immersion in the name of the Father, the Son, and the Holy Spirit.