The cursive and ligature nature of the Arabic script make the segmentation of words into individual characters a difficult task. Despite attempts to apply methods for cursive Latin and other scripts to Arabic script, it is generally insufficient to segment the Arabic text. This paper proposes a new segmentation algorithm for the handwritten Arabic text and the main idea consists of segmenting the word into sub-words and then computing the baseline of each sub-word. Using the descenders of sub-words and the baseline, candidate points are then calculated using a vertical projection. The algorithm has been tested using 800 handwritten Arabic words taken from the IFN/ENIT database and a comparison made against some existing methods and promising results have been obtained.