The transfer matrices which have been used in previous studies on the one-dimensional bond percolation problem with bonds connecting Lth nearest neighbours are only for the case of directed bonds. For the case of undirected bonds, the transfer matrices are non-systematic and become much more complicated when L>or=3. Here the authors study the cases of L=2, 3 and find that the critical behaviour remains unchanged. They strongly suggest that this is true for any L. Rigorous evidence is given to support this conjecture.