In the article the Markushevich boundary problem on the circle is considered for the case when the first coefficient of the problem is an arbitrary function from the Holder class and the second coefficient is the boundary value of a function that is meromorphic in the unit disk. An explicit method of solution of the given problem is proposed, the number of linearly independent solutions of the homogeneous problem and the number of solvability conditions are calculated, the general solution of the problem is found.
