The study of cellular membrane proteins calls for computational tools to elaborate their structure, using their amino-acid sequence alone. Unfortunately, even today, it is very difficult to solve their 3-D structure by X-ray crystallography or NMR. Thus, several methods have been invented to detect their transmembrane regions. In addition, their orientation through the membrane (topology) needs to be determined, that is, the direction of each transmembrane segment (towards the inner part of the cell or vice-versa). OrienTM is a computer software (written in C++) that predicts the orientation for both the whole molecule, and for each region of it independently. It uses "position specific" statistical analysis of the amino-acid residues in the non-transmembrane regions of every membrane protein in the SwissProt database. It is based on a stable statistical algorithm, without integrating empirical observations or arbitrarily optimizing the results. The success levels are quite satisfactory for standard protein sets with known structures taken from the literature (100% for a sample of 80 eukaryotic proteins), and for the whole SwissProt as well (95.43% in eukaryotic proteins). In most cases they are higher than those achieved by the empirical Positive Inside rule (the most common method nowadays). The program may freely be used through the Internet, at the address http://biophysics.biol.uoa.gr/orienTM utilizing any navigation tool (e.g. Netscape, Internet Explorer).