Digital image correlation (DIC) is commonly used to measure specimen displacements by correlating an image of a specimen in an undeformed or reference configuration and a second image under load. To establish the correlation between the images, numerical techniques are used to locate an initially square image subset in a reference image. In this process, choosing appropriate coordinates is of fundamental importance to ensure accurate results. Both global and local coordinates can be used in shape functions. However, large rigid body rotations and deformations are accurately obtained by using global rather than local shape functions. In addition, points located after displacement may not be at an integer pixel distance from the original position. Hence subpixel displacement estimation methods such as interpolation or fitting of correlation coefficients are essential. A solution using the least-squares method is employed by choosing proper coordinates, and the feasibility of using local coordinates is demonstrated and validated with a mathematical model. Both simulated and experimental results show that the proper choice of coordinates does ensure the reliability and improve the accuracy of measurements in DIC.