In this paper we introduce a measure of magnetic field discontinuity, MAD, defined as Maximum Angular Difference between two adjacent magnetic field vectors. To examine the characteristics of the MAD, we have considered several active region models having a quadrupolar field configuration and computed MADs over these active regions by approximating the 3-D magnetic fields as an ensemble of charge potential fields or linear force-free fields. The computed MAD fields are studied in comparison with other flare activity indicators such as separators. It is found that (1)the region of high level MAD corresponds well with the separator, or practically the intersection of the separator with the plane of measurement, (2)it singles out local discontinuities of magnetic fields, and (3)the MAD can also be a measure of the evolutionary status of an active region. An observational test has been made for 2-D MADs, using the Yohkoh SXT observation of a flare in AR6919 and the vector magnetogram taken at the Mees Solar Observatory during this flare activity. The high level contours of 2-D MAD are found to trace well the observed soft X-ray bright points, which indicates that the MAD could serve as a good flare activity indicator.