Electromagnetic surface waves guided by the planar interface of an isotropic dielectric medium and a uniaxial dielectric medium, both non-dissipative, were considered, the optic axis of the uniaxial medium lying in the interface plane. Whereas this interface is known to support the propagation of Dyakonov surface waves when certain constraints are satisfied by the constitutive parameters of the two partnering mediums, we identified a different set of constraints that allow the propagation of surface waves of a new type. The fields of the new surface waves, named Dyakonov–Voigt (DV) surface waves, decay as the product of a linear and an exponential function of the distance from the interface in the anisotropic medium, whereas the fields of the Dyakonov surface waves decay only exponentially in the anisotropic medium. In contrast to Dyakonov surface waves, the wavenumber of a DV surface wave can be found analytically. Also, unlike Dyakonov surface waves, DV surface waves propagate only in one direction in each quadrant of the interface plane.