This paper presents a simple approach to evaluate origin intensity factors of the singular boundary method (SBM), a recent strong-form boundary discretization numerical technique. The SBM overcomes the perplexing 'fictitious boundary issue' associated with the method of fundamental solutions (MFS) and in it the source points and collocation points coincide on the real physical boundary. By analogy with the boundary element method (BEM), we develop a desingularization strategy for the direct computation of singular kernels in the SBM, without losing the merits of being truly meshless, integration-free, and easy-to-implement. In addition, an efficient non-linear co-ordinate transformation is employed to tackle the near singularities of the kernel functions, when the calculation point is close to, but not on, the boundary. It is shown that the proposed SBM fully inherits the merits of the BEM and MFS. The advantages, disadvantages and potential applications of the proposed method, as compared with the MFS and the BEM, are also examined and discussed in detail.