We study the classical solution of the nonlinear inverse boundary value problem for for pseudo hyperbolic equation of the fourth order The essence of the problem is that it is required together with the solution to determine the unknown coefficient. The problem is considered in a rectangular area. To solve the considered problem, the transition from the original inverse problem to some auxiliary inverse problem is carried out. The existence and uniqueness of a solution to the auxiliary problem are proved with the help of contracted mappings. Then the transition to the original inverse problem is made, as a result, a conclusion is made about the solvability of the original inverse problem