Gasyuto was at Lokomotiv-96 Vitebsk in 2000 and had a two-month spell at FC Molodechno 2000 this season. Recently the 49-year-old was working as an assistant coach at third division FC Osipovichi.
Belshina are seventh in the table having collected just two points from seven games, but Gasyuto said: "The task of safeguarding our place in the top flight does not seem impossible to me. However, I need time to look closely at my players, to learn their abilities." Belshina will travel to fourth-placed local rivals FC Torpedo Zhodino on 6 June.
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