Digital Image Correlation (DIC) is an easy to use yet powerful approach to measure displacement and strain fields. While the method is robust and accurate for a variety of applications, standard DIC returns large error and poor correlation quality near displacement discontinuities such as cracks or shear bands. This occurs because the subsets used for correlation can only capture continuous deformations from the reference to the deformed image. As a result the regions around discontinuities are typically removed from the area of interest, before or after analysis. Here, a novel approach is proposed which enables the subset to split in two sections when a discontinuity is detected. This method enables the measurement of “displacement jumps”, and also of displacements and strains right by the discontinuity (for example a crack profile or residual strains in the wake). The method is validated on digitally created images based on mode I and mode II asymptotic displacement fields, for both sub-pixel and super-pixel crack opening displacements. Finally, an actual fracture experiment on a high density polyethylene (HDPE) specimen demonstrates the robustness of the method on actual images. Compared to other methods capable of handling discontinuities, this novel “subset-splitting” procedure offers the advantage of being a direct extension of the now popular standard DIC, and can therefore be implemented as an “upgrade” to that method.