The present paper is devoted to the search for the polarimetric sensitivity level in observations of the Fe i 5576Å line performed with the THEMIS spectropolarimetric mode MTR on August 23 1998. This line is insensitive to the Zeeman effect and the present work is thus useful to calibration purposes. The upper level of the line is unpolarizable (J = 0) and insensitive to the Hanle effect, and the observations have been performed at disk center to avoid any scattering polarization of lower level atomic polarization origin. In the present paper, we describe the steps of a method that is the basis of a data reduction code implemented on systems at the Meudon Observatory for the interpretation of observations where a large number (∼150) of images are averaged, and where the signal is in addition averaged along the slit. First, we describe the numerical methods used to determine the line position in the images, and to perform operations on the profiles by FFT techniques (such as translation, dilation, defocusing, apodization). Then, the preprocessing steps are described: dark current subtraction, destretching and flat-field correction. The polarization analysis is then performed, based on the idea that, as the flat-field images are unpolarized, they can be used to correct spurious polarization occuring in the observations. As a result, the observed line is found to be unpolarized, and a sensitivity of 2-4×10 −4 is found for the polarization degree in the neighboring continuum.