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In this paper, an effective method to obtain all nonnegative integer minimal support vectors (U4,V4) at level 4 for an arbitrary homogeneous/inhomogeneous solution starting from nonnegative rational number minimal support vectors (U3,V3) at level 3 is proposed. Although V4 has been derived from all minimal vectors (U5,V5) of level 5 which are obtained starting from vectors at level 1, 2, or 3, so far. This proposed method for (U4,V4) gives us a big shortcut comparing with them. However, it is pointed out that obtaining (U5,V5) of level 5 from (U4,V4) of level 4 is not so wise.