Abstract: The singular boundary method (SBM) is a relatively new meshless boundary collocation method for the numerical solution of certain boundary value problems. The key idea is to introduce the concept of the origin intensity factor to isolate the singularity of the fundamental solutions, so that the source points directly coincide with the collocation points on the realistic boundary. This overcomes a perplexing fictitious boundary outside physical domain in the recently popular method of fundamental solutions (MFS). However, the inverse interpolation technique requires the placement of a cluster of sample nodes inside or outside the physical domain for either interior or exterior problems. Our recent numerical experiments indicate that the overall accuracy of this SBM formulation is, to a certain degree, sensitive to the location of such sample nodes. To remedy the above-mentioned drawbacks, this paper proposes an improved SBM formulation for three-dimensional potential problems to circumvent sample nodes in the inverse interpolation technique with the traditional SBM. Numerical experiments demonstrate its significantly improved accuracy and stability in comparison with the traditional SBM formulation.