A digital gray scale image generally consists of 256 different gray tones. Printers and image setters normally generate much fewer levels and mostly only two levels. Therefore, in order to be able to display a digital cone-tone image by a multilevel device it has to be transformed into an image with fewer levels. The technique doing this transformation is called multi-level halftoning, and in the case of bilevel devices it is simply called halftoning. In this paper we propose a novel (bilevel) halftoning technique that is based on multilevel halftoning. The proposed method can also be categorized as belonging to hybrid amplitude modulated (AM)/ frequency modulated (FM) techniques. In this method the original digital image is firstly halftoned by a multilevel FM halftoning. Each level in the multilevel halftoned image is then replaced by a halftone table (microcell). An approach for extending any bilevel FM halftoning method to a multilevel method is also presented in this paper. The performance of the proposed method is examined by a number of illustrations where nonmodified error diffusion and our FM method are used. The problem with maze-like artifacts that occur when our FM halftoning, or similar methods such as DBS, are used as the macroscreen is discussed and a simple solution is introduced. An approach for extending the proposed method to be used in situations where the halftone dots cannot be produced smaller than a specific size is also proposed and examined. This modified version of the method can be useful for flexography, where the dots normally cannot be produced smaller than a critical size.