dWe have succeeded to prepare high resistivity and rather low dielectric constant amorphous carbon nitride films a-CNx (0.52<x<0.86) by the reactive radio frequency magnetron sputtering of a graphite target using nitrogen molecules as a sputter gas. The resistivity of a-CNx are 5x10(16) to 10(17)Omega-cm and be estimated to 10(20)Omega-cm, when the ratio of the carbon and nitrogen becomes chemically stoichiometry 3 to 4, i.e. C3N4. The resistivity of a-CNx films prepared by a layer-by-layer method, LL-a-CNx, is 10(18)Omega-cm for x=0.6. The layer-by-layer method is a cyclic process of a deposition by the sputtering and an etching by atomic hydrogen. The sample LL-a-CNx made by a layer-by-layer method are compared with that of usual method a-CNx. The dielectric constant of a-CNx films calculated from the refractive index n are 3.6 to 2.8 corresponds to nitrogen contents, 0.52<x<0.86. The dielectric constants epsilon of a-CNx films decrease with the content of nitrogen x. At an ultimate component of a-CNx at x=4/3, the dielectric constant is estimated to 1.8.