A number of authors have shown that the N-soliton solution of the KdV equation can be decomposed into N separate soliton elements. However, it is not immediately clear from the form of these solutions how the separate soliton elements relate directly to the solitary wave (or single soliton) solution. In a previous paper by the authors it was shown how the two-soliton solution can be written in a form such that its relationship to the solitary wave is clearly apparent, and the utility of this special formulation of the solution was demonstrated in analysing the structure during interaction of the two-soliton solution of the KdV equation. Here it is shown how to generalize that result to the N-soliton case, and some examples are given of how this formulation of the solution is useful in analysing properties of the N-soliton interaction for the cases \(N=3,4\).