A new method of mapping molecular electrostatic potentials using a dipole of arbitrary length and strength has been developed. The dipole is allowed to move on a geometrical surface enclosing the molecule under study such that the closest distance of approach (CDA) between the two species is fixed. Potential maps of water, formaldehyde and ethylene epoxide molecules have been studied by this approach for CDA values of 2 and 5 A. Experimental geometries for the molecules and net charge distributions obtained by the MNDO molecular orbital method were used in the calculations. Dipole potential maps obtained by the present method are compared with those obtained by the prevalent monopole mapping method. The two approaches broadly predict the same sites for potential minima in the molecules studied. The present dipole maps are however more informative, especially with regard to electric field directions, than the monopole maps, and it has been shown that this additional information is very useful.