For 1 ≤ k≤ n-1, the existence of solutions to the singular boundary value problem are reestablished under weaker and fewer restrictions on f(t, y), where f(t, y) may be singular at y = 0, t = 0 and t = 1. The arguments involve only positivity properties of the Green's function and a fixed point in cones. Moreover, the explicit formula of Green's function can be found in this paper.