The integral equation \(f(x)=\lambda \int^{x+1}_{x-1}K(x,y)f(y)dy\quad for\quad x\geq 1\) with the additional condition \(f(x)=\psi(x),\) \(0\leq x<1\), where K(x,y) and \(\psi(x)\) are given real functions, is considered. By reducing the problem to an operator equation in a Banach space, the author establishes the existence of a unique solution of the problem for sufficiently small \(\lambda\). An algorithm to solve numerically this problem is proposed. As an example, the special problem to find a binary correlation function for the set of circles on the plane is considered in details. Here \(K(x,y)= y \arccos((x^ 2+y^ 2-1)/2xy),\) \(\psi(x)=-1\).