Theory of the propagation of a surface wave related both to Bleustein‐Gulyaev waves and Love waves is developed. The wave has unidirectional particle motion perpendicular to the direction of propagation and parallel to the surface of a piezoelectric material which is covered with a finite‐thickness layer of an isotropic conducting material. An equation relating phase velocity to material costants is solved in closed form for a piezoelectric material of class 6mm, and conditions for the existence of various modes are presented. Piezoelectricity allows a nonleaky but dispersive wave to exist under conditions is which no love wave is possible, namely, when the shear wave velocity in the layer is greater than that in the substrate. Numerical results are presented for aluminium, gold, and zinc layers on PZT 4 ceramic.