A new kind of stripline microwave high pass filter is proposed in this paper. Striplines here used have a tapered inner conductor and are filled by inhomogeneous dielectric materials with continuous spatial variation of the refraction index. Thus, filtering properties of such components can be controlled by means of two different keys: the inner conductor taper and the refraction index spatial variation of the dielectric material filling the stripline. A design method for such a filter is carried out starting from the generalized nonuniform transmission line theory by which a novel closed analytical form for the input reflection coefficient is derived. This closed form allows to obtain straightforwardly the design formulas for the high pass filters. Finally, some applications that show the capability of the new filter here proposed and the fastness of the developed synthesis method are presented.