A novel three-part expression for nonsymmetrical components of the dyadic Green's function of a multilayer medium is derived. This new expression provides a very accurate and computationally fast method for calculation of such components. Several sets of numerical data are also presented and discussed. A new expression based on a quasistatic approach is derived for near-field regions. This expression provides an insight into the behaviour of nonsymmetric components of vector potential for the cases where the source and field points approach each other in multilayer media.