A fast line segment detection method, unite-and-divide (UND) approach, is investigated, which includes two phases, namely the union of spectra in the frequency domain and the division of the sinogram in Radon space respectively. In the union phase, for a given image, its sinogram is obtained by parallel 2D multilayer Fourier transform, Cartesian-to-polar mapping and 1D inverse Fourier transform. In the division phase, every peaks and edges of butterfly wings in its neighborhood in sinogram are firstly specified, with each neighborhood area corresponding to a window in image space, and then, by applying edge-analyzing to each sinogram of each windowed separately, the endpoints of line segments are extracted. Our experiments are conducted on benchmark images, the results reveal that the UND method yields high accuracy, low computational cost and is more robust to noise.