McBride and McStay have both left the Budapest club
Former Celtic reserve team boss Willie McStay has resigned as Ujpest's head coach amid reports of financial difficulties at the Hungarian club.
Zoltan Kovacs, Ujpest's director of football, told the club's official website: "Willie McStay has resigned from the position.
"Both the club and Willie mutually agreed in an amicable way."
McStay left Celtic for Ujpest last summer following the arrival of Tony Mowbray as manager.
Reports suggested at the time that it was part of an international exchange programme in which Ujpest would be utilised as a feeder club for the Glasgow club.
McStay, the brother of former Celtic midfielder Paul, made 65 league appearances for Celtic between 1979 and 1987 and had spells with Huddersfield Town, Notts County and Hartlepool United.
He was player-manager of Sligo Rovers from 1992 to 1994 before taking on the reserve coaching role at Celtic.
His 15 years at Celtic, during which they won eight reserve titles in a row, came to an end a couple of weeks after Mowbray's arrival.
However, Mowbray was sacked last month, with Neil Lennon, who had been McStay's successor as reserve team coach, being promoted to interim manager until the end of the season.
McStay leaves Ujpest sitting sixth in the Hungarian top flight, dropping a place after a 1-0 defeat by relegation-threatened Szombathelyi Haladas.
"Joe McBride has also resigned from his position of coach and Ujpest Football Club would like to thank both Willie McStay and Joe McBride for the hard work and effort that they put into their jobs while at the club," added Kovacs.
"Ujpest wish both of them every success in their football careers ahead."
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