Corner detection is a fundamental step for many computer vision applications to detect the salient image features. Recently, FAST corner detector has been proposed to detect the high repeatable corners with efficient computational time. However, FAST is very sensitive to noise and detects too many unnecessary corners on the noise or texture region. In this paper, we propose a robust corner detector improved from FAST in terms of the localization accuracy and the computational time. First, we construct a gradient map using the Haar-wavelet response by integral image for efficiency. Second, we define a corner candidate region which has large gradient magnitude enough to be corner. Finally, we detect the corner on the corner candidate region by FAST. Experimental results show the proposed method improves localization accuracy measured by the repeatability than standard FAST and the-state-of-art methods. Moreover, the proposed method shows the best computation efficiency. Especially, the proposed method detects the corners more accurately in the image containing many texture regions and corrupted by the Gaussian noise or the impulse noise.