Abstract: We considered necessary and sufficient conditions for the Verma modules M(μ(u)) of twisted Yangian Y(o₂)  to be reducible. If the weight of M(μ(u)) was determined by a certain rational function,  we could obtain a proper submodule of M(μ(u)) through construction method, thus proving  that M(μ(u)) was reducible. If M(μ(u)) was reducible, we could obtain a rational function associated with u，thus  we gave a necessary condition for M(μ(u)) to be reducible was that the rational function was a Laurent expansion at u=∞.

Key words: twisted Yangian, Verma module, reducibility