Positive solutions are obtained for the fourth order nonlocal boundary value problem, u(4)=f(x,u), 0 \u3c x \u3c 1, u(0) = u\u27\u27(0) = u\u27(1) = u\u27\u27(1) - u\u27\u27(2/3)=0, where f(x,u) is singular at x = 0, x=1, y=0, and may be singular at y=∞. The solutions are shown to exist at fixed points for an operator that is decreasing with respect to a cone