Measuring the thickness of different corneal microlayers is important for the diagnosis of common corneal eye diseases such as dry eye, keratoconus, Fuchs endothelial dystrophy, and corneal graft rejection. High resolution corneal images, obtained using optical coherence tomography (OCT), made it possible to measure the thickness of different corneal microlayers in vivo. The manual segmentation of these images is subjective and time consuming. Therefore, automatic segmentation is necessary. Several methods were proposed for segmenting corneal OCT images, but none of these methods segment all the microlayer interfaces and they are not robust. In addition, the lack of a large annotated database of corneal OCT images impedes the application of machine learning methods such as deep learning which proves to be very powerful. In this paper, we present a new corneal OCT image segmentation algorithm using Randomized Hough Transform. To the best of our knowledge, we developed the first automatic segmentation method for the six corneal microlayer interfaces. The proposed method includes a robust estimate of relative distances of inner corneal interfaces with respect to outer corneal interfaces. Also, it handles properly the correct ordering and the non-intersection of corneal microlayer interfaces. The proposed method was tested on 15 corneal OCT images that were randomly selected. OCT images were manually segmented by two trained operators for comparison. Comparison with the manual segmentation shows that the proposed method has mean segmentation error of 3.77±4.25 pixels across all interfaces which corresponds to 5.66 ± 6.38μm. The mean segmentation error between the two manual operators is 4.07 ± 4.71 pixels, which corresponds to 6.11 ± 7.07μm. The proposed method takes a mean time of 2.59 ± 0.06 seconds to segment six corneal interfaces.