The　major　problem　in　applying　a　meshless　(RPIM)　method　is　that　when　a　large　number　of　sampling　nodes　is　used,　the　condition　number　of　the　moment　matrix　increases,　and　numerical　solution　becomes　unstable　due　to　the　required　inversion　of　the　matrix.　To　address　the　problem,　in　this　paper,　with　the　radial　point　interpolation　meshless　(RPIM)　method　as　an　example,　the　moment　matrix　is　first　diagonalized　and　then　the　associated　singular　eigenvalues　that　cause　the　instability　are　truncated.　As　a　result,　the　dependence　of　the　stability　on　the　number　of　the　sampling　nodes　is　removed.　Numerical　experiments　are　conducted,　and　the　results　have　shown　that　the　proposed　algorithm　are　stable　irrespective　of　number　of　sampling　nodes;　they　pay　the　way　forward　for　the　meshless　method　to　be　applied　to　practical　structures.