The skeleton and the skeleton function of an object are important representations for shape analysis and recognition. They contain enough information to recognize an object and to reconstruct its original shape. However, they are sensitive to distortion caused by rotation and noise. This paper presents another approach for binary object representation called a modified exoskeleton(mES) that combines the previously defined exoskeleton with the use of symmetric object whose dominant property is rotation invariant. The mES is the skeleton of a circular background around the object that preserves the skeleton properties including significant information about the object for use in object recognition. Then the matching algorithm for object recognition based on the mES is presented. We applied the matching algorithm to evaluate the mES against the skeleton obtained from using 4-neighbor distance transformation on a set of artificial objects, and the experimental results reveal that the mES is more robust to distortion caused by rotation and noise than the skeleton and that the matching algorithm is capable of recognizing objects effectively regardless of their size and orientation.