nonlinear deformations can irreversibly alter the mechanical properties of materials. most soft materials, such as rubber and living tissues, display pronounced softening when cyclically deformed. Here we show that, in contrast, reconstituted networks of crosslinked, bundled actin filaments harden when subject to cyclical shear. As a consequence, they exhibit a mechanomemory where a significant stress barrier is generated at the maximum of the cyclic shear strain. This unique response is crucially determined by the network architecture: at lower crosslinker concentrations networks do not harden, but soften showing the classic mullins effect known from rubber-like materials. By simultaneously performing macrorheology and confocal microscopy, we show that cyclic shearing results in structural reorganization of the network constituents such that the maximum applied strain is encoded into the network architecture.