This is the continuation of the earlier work of the author and H. Liu [A generalized Riemann boundary value problem, Wuhan Univ. J. Nat. Sci. 5, No. 2, 147–149 (2000; Zbl 1044.30508)]. Let \(L\) be a smooth closed contour in the complex plane. The author in a Hölder function space considers the Riemann boundary value problem \[ \sqrt{\psi^-(t)}= G(t)\sqrt{\psi^-(t)}+ g(t),\quad t\in L \] under weaker conditions.