We present an algorithm for calibrated camera relative pose estimation from lines. Given three lines with two of the lines parallel and orthogonal to the third we can compute the relative rotation between two images. We can also compute the relative translation from two intersection points. We also present a framework in which such lines can be detected. We evaluate the performance of the algorithm using synthetic and real data. The intended use of the algorithm is with robust hypothesize-and-test frameworks such as RANSAC. Our approach is suitable for urban and indoor environments where most lines are either parallel or orthogonal to each other.