The eye tracking technology is used for four decades for studying reading behavior. The applications are various: estimating the reader comprehension, identifying the reader, summarizing a read document, creating a reading-life log, etc. The gaze data used in such applications has to be accurate enough to perform the analysis. In order to improve the accuracy, most of the experiments are set up with restrictive conditions such as using a head fixation and a professional eye tracker. It implies that the results are valid only in restrictive laboratory settings and an unrealistic small error is produced by the experiment. However, the use of affordable eye trackers in realistic conditions of reading leads to large errors in the recordings. We propose a new algorithm to correct the vertical error and to align the gazes with the text. The proposed algorithm is robust to rereading and skipping some parts of text, contrary to all the other algorithms of the state of the art. We show that up to 69 % of the gazes are aligned with the correct text lines.