Halftoning is an important process to convert a gray scale image into a binary image with black and white pixels. The Direct Binary Search (DBS) is one of the well-known halftoning methods that can generate high quality binary images for middle tone of original gray scale images. However, binary images generated by the DBS have clippings, that is, have no tone in highlights and shadows of original gray scale images. The first contribution of this paper is to show the reason why the DBS generates binary images with clippings, to clarify the range of tone in original images that may have clipping, and to present a clipping-free DBS-based halftoning algorithm. The key idea is to apply the ordered dither using a threshold array generated by DBS-based method, to highlights and shadows, and then use the DBS. The second contribution is to extend the DBS to generate L-level multitone images with each pixel taking one of the intensity levels , , ..., . However, clippings appear in highlights, middle tone, and shadows of generated L-level multitone images. The third contribution of this paper is to modify the multitone version of the DBS to generate a clipping-free L-level multitone images. The resulting multitone images are so good that they reproduce the tones and the details of the original gray scale images very well.