The Method of Fundamental Solution applied to the Stokes equation is investigated. Instead of using the classical approach, the problem is split into several subproblems defined on much smaller subdomains. Each local problem is solved by the Method of Fundamental Solutions. Having solved the local problems, the approximate solution is updated at the central point of the local subdomain. This results in a Seidel-like iterative method, which mimics the classical overlapping Schwarz method. In contrast to the traditional Method of Fundamental Solutions, the resulting localized method avoids the problem of large, dense and ill-conditioned linear systems of equations, and, at the same time, remains a truly meshfree technique.