Research on boundary value problems for systems of first-order partial differential equations with singular coefficients developed in two directions, in one of which the objects of study were coefficients with singular points, in the other - with singular lines. In this paper, the problem for the Beltrami equation with a polar singularity in an unbounded domain is solved. The coefficients of the equation  have a first-order pole at z = 0 and do not even belong to the class  For this reason, despite its specific form, this equation is not covered by the analytical apparatus of I.N. Vekua and needs to be independently studied. To find a solution to the problem, the method developed by A.B.Tungatarov in combination with the methods of theories of functions of complex variable and functional analysis was used. The dependence of the conditions of smallness of the coefficients of the equations on the area  was eliminated; the equations were studied only in the neighborhood of singular points. As a result of this work, a sufficient condition for solvability of the initial boundary value problem for the Beltrami system with polar singularity is found.