Previously, the author has proven [Algebra Logika 35, No. 1, 105-117 (1996; Zbl 0897.03022)] that the interpolation property is missing in all predicate superintuitionistic logics which contain the logic \(J^*_{fd}\) (characterized by all Kripke frames whose domains of all nonmaximal worlds are finite) and are contained in a logic specified by all two-element frames with finite constant domains. In the article under review, it is shown that the logic \(J^*_{fd}\) lacks the Beth property. The logic is the first example of an intermediate superintuitionistic logic without the Beth property. The interpolation and the Beth properties are also proven missing in all predicate superintuitionistic logics which contain the logic \(J^{*}_{fd}\) and are contained in the logic characterized by frames of the form \(\langle N_n,\leq \{D_k\}_{k\in N_n}\rangle\).