Summary: A functional model for any bounded non-selfadjoint operator in a Hilbert space \(H\) is constructed. The operator dissipative property is not supposed to be fulfilled. This model is a generalization of the functional model of B.S.Pavlov [Transl., Ser.2, Am.Math.Soc.115, 103–142 (1981); translation from Proc.7th Winter School, Drogobych 1974, 3–69 (1976; Zbl 0516.47007)] and realized by the operator of multiplication by the independent variable in a weighted Hardy space in a strip.