The fuzzy assignment model depicts a special case of fuzzy linear programming problem (F.L.P.P) in which the objective is to assign the number of origins to the same number of destinations at minimum total cost. The fuzzy assignment should be framed on one-to-one basis. In this research article it is developed a method using the Branch and Bound Technique has been developed for symmetric fuzzy assignment (equally spread) of jobs. Also in this method fuzzy optimal solution has been obtained without converting the symmetric fuzzy assignment problem (equally spread) as a crisp. © Published under licence by IOP Publishing Ltd.