The orientation of fibrils within biological tissues is of primary importance. In this study, we propose a simple method based on second harmonic generation (SHG) microscopy to map, pixel by pixel, the orientation of the symmetry axis of the second-order nonlinear susceptibility tensor of fibrils that produce SHG. The method uses only four images acquired at specific polarizations of the input laser beam, and can be easily and cheaply implemented on a confocal microscope. In addition to orientation informations, the method also provides polarization independent images and estimations of the ratio of the nonlinear susceptibility components. We demonstrate the relevance of our concept by studying the orientation fields of the collagen meshwork in a healthy rat liver that provides well separated fibrils. By correlating the mean orientation of the nonlinear susceptibility to the fibril orientation itself for many fibril segments, and using circular statistics, it is shown that both orientations are truly parallel at the fibril scale. Our polarimetric method allows to map fibril orientation fields, independently of individual fibril contrast in the SHG image.