Wavefront shaping through multimode fibers has many interesting applications, such as micromanipulation and endoscopy, where the small diameter of fibers is an advantage in terms of miniaturization. However, pattern projection can suffer from deleterious interference effects depending on the measurement conditions. We experimentally demonstrate the projection of high quality patterns through a multimode fiber by correcting for phase drifts while measuring the transmission matrix, and by controlling both the amplitude and the phase of the wavefront sent to the fiber. We also use the matrix in the reverse direction by reconstructing a distal image from a proximally measured speckle field. This opens up new possibilities for imaging through a multimode fiber by decoding wavefronts travelling both ways along the fiber.