The conventional resolution of transmission electron microscopes is orders of magnitude larger than the wavelength of the electrons used. Aberrations of the objective lens corrupt spatial information on length scales below a limit known as the point resolution. Methods to correct for lens aberrations require knowledge of the phase of the waves which make up the image (this constitutes the 'phase problem'). Beyond the point resolution, information can still be transferred by the microscope, but partial coherence of the scattered beams imposes an ultimate limit (the 'information limit') on the resolution of the transferred image information. Here we show that this limit can be overcome to obtain images of still higher resolution with a scanning transmission electron microscope. Our approach involves collecting coherent microdiffraction patterns as a function of probe position, enabling us to extract the phase differences of all neighbouring pairs of diffracted beams. Using this approach for a microscope with a conventional point resolution of 0.42 nm and a conventional information limit of 0.33 nm, we are able to form an aberration-free image that resolves an atomic spacing of 0.136 nm.