This document reports the first results and their interpretation of the straw straightness measurements that have been performed on the first 4-plane end-cap prototype of the ATLAS TRT. Section 2 presents the experimental setup used for the measurements, as well as a review of the data sample used to perform this study. It also provides a description of the method used to assess straw straightness, which is based on the measurements of the maximal gas gain deviation (``straw eccentricity'') seen along the straw. Section 3 reports the results of straw straightness for the 4-plane module, including corrections due to the gas flow. The effect of energy resolution degradation is also explained and results in terms of wire offset are reported. In Section 4, the straw bending due to an applied lateral deformation is measured, and finally Section 5 reviews the conclusions.