Contour map has contour lines that are significant in building a Digital Elevation Model (DEM). During the digitization and pre-processing of contour maps, the contour line intersects with each other or break apart resulting in broken contour segments. These broken segments impose a greater risk while building DEM leading to a faulty model. In this project, a simple yet efficient mechanism is used to match and reconnect the endpoints of the broken segments accurately and efficiently. The matching of the endpoints is done using the concept of minimum Euclidean distance and gradient direction while the Cubic Hermite spline interpolation technique is used to reconnect the endpoints by estimating the values using a mathematical function that minimizes overall surface curvature resulting in a smooth curve. The purpose of this work is to reconnect the broken contour lines generated during the digitization of the contour map, to help build the most appropriate digital elevation model for the corresponding contour map.