A composite seal face ring has an inner ring (60) made of material with good tribological properties, the inner ring (60) being pre-compressed by an outer ring (64) with a high tensile strength and a thermal coefficient of expansion substantially equal to that of the inner ring (60). The seal face ring is assembled by compressing the inner ring (60) and/or expanding the outer ring (64) by fluid under pressure, before inserting the inner ring (60) into the outer ring (64).