Past research has demonstrated that digital Fresnel holograms can be binarized in a non-iterative manner by downsampling the source image with a grid lattice prior to the hologram generation process. The reconstructed image of a hologram that is binarized with this approach is superior in quality compared with that obtained with direct thresholding, half-toning, and error diffusion. Despite the success, the downsampling mechanism results in a prominent texture of regularly spaced voids in the shaded regions. To alleviate this problem, an enhanced non-iterative method for the generation of binary Fresnel holograms is presented. Our method is based on a multi-direction line-sampling formed by a combined grid and cross lattice, which is capable of preserving a more solid texture in the shaded regions and enhancing the visual quality of the reconstructed image. Computer simulations and optical reconstructions are shown to demonstrate the effectiveness of our proposed technique.