Film dosimetry using radiochromic EBT film in combination with a flatbed charge coupled device scanner is a useful method both for two-dimensional verification of intensity-modulated radiation treatment plans and for general quality assurance of treatment planning systems and linear accelerators. Unfortunately, the response over the scanner area is nonuniform, and when not corrected for, this results in a systematic error in the measured dose which is both dose and position dependent. In this study a novel method for background correction is presented. The method is based on the subtraction of a correction matrix, a matrix that is based on scans of films that are irradiated to nine dose levels in the range 0.08-2.93 Gy. Because the response of the film is dependent on the film's orientation with respect to the scanner, correction matrices for both landscape oriented and portrait oriented scans were made. In addition to the background correction method, a full dose uncertainty analysis of the film dosimetry procedure was performed. This analysis takes into account the fit uncertainty of the calibration curve, the variation in response for different film sheets, the nonuniformity after background correction, and the noise in the scanned films. The film analysis was performed for film pieces of size 16 x 16 cm, all with the same lot number, and all irradiations were done perpendicular onto the films. The results show that the 2-sigma dose uncertainty at 2 Gy is about 5% and 3.5% for landscape and portrait scans, respectively. The uncertainty gradually increases as the dose decreases, but at 1 Gy the 2-sigma dose uncertainty is still as good as 6% and 4% for landscape and portrait scans, respectively. The study shows that film dosimetry using GafChromic EBT film, an Epson Expression 1680 Professional scanner and a dedicated background correction technique gives precise and accurate results. For the purpose of dosimetric verification, the calculated dose distribution can be compared with the film-measured dose distribution using a dose constraint of 4% (relative to the measured dose) for doses between 1 and 3 Gy. At lower doses, the dose constraint must be relaxed.