Hand gesture recognition is an important area of research in the field of Human Computer Interaction (HCI). The geometric attributes of the hand play an important role in hand shape reconstruction and gesture recognition. That said, fingertips are one of the important attributes for the detection of hand gestures and can provide valuable information from hand images. Many methods are available in scientific literature for fingertips detection with an open hand but very poor results are available for fingertips detection when the hand is closed. This paper presents a new method for the detection of fingertips in a closed hand using the corner detection method and an advanced edge detection algorithm. It is important to note that the skin color segmentation methodology did not work for fingertips detection in a closed hand. Thus the proposed method applied Gabor filter techniques for the detection of edges and then applied the corner detection algorithm for the detection of fingertips through the edges. To check the accuracy of the method, this method was tested on a vast number of images taken with a webcam. The method resulted in a higher accuracy rate of detections from the images. The method was further implemented on video for testing its validity on real time image capturing. These closed hand fingertips detection would help in controlling an electro-mechanical robotic hand via hand gesture in a natural way.