Theorem: Let A be an analytic curve defined in a neighbourhood of a polydisk \(D^ n\) such that: (i) The singular points of A are situated strictly inside \(D^ n\); (ii) The intersection of A with each \(\Gamma_ i:=D_ 1\times...\times D_{i-1}\times\partial D_ i\times D_{i+1}\times...\times D_ n\) or \(\Gamma_{ij}:=\Gamma_ i\cap\Gamma_ j\) is transversal at every point. Then there exists a continuous linear extension operator \(L: H^{\infty}(A)\to H^{\infty}(D^ n)\) (here \(H^{\infty}\) stands for the space of bounded holomorphic functions). Moreover, if \(g\in H^{\infty}(A)\) is continuous on \(A\cap\bar D^ n\), then L(g) is continuous on \(\bar D\). A sketch of proof based on a technique developed by \textit{G. M. Khenkin} [Izv. Akad. Nauk SSSR, Ser. Mat. 36, 540-567 (1972; Zbl 0249.32009)] is given.