The paper deals with the singular integral equation
$$a(t)\varphi(t)+b(t)[S+MP_{\ell}\varphi](t)=f(t),$$
where $a(t) =\prod_{i=1}^m(t-\alpha_i)^{r_i}s(t)$. We will reduce the equation to the well-known Riemann boundary value problem and then describe all solution of the indicate problem in a closed form.