The author offers a new approach to solution of the Riemann–Hilbert boundary value problem for analytic function in multiconnected
circular domain. This approach is based on construction of solution of corresponding homogeneous problem, when analytic in domain
function is being defined by known boundary values of its argument. The author considers a special case of a problem when the
index of a problem is more than zero and on unit of less order of connectivity of domain. Resolvability of a problem depends on
