Buildings constructed of reinforced concrete frames with masonry infill (RCFMI) are comprised of unreinforced masonry walls that are tightly infilled into the space between the reinforced concrete frames. Poor seismic performance of RCFMI buildings has been observed during past earthquakes and it has been repeatedly acknowledged that damage to masonry infills, in many cases, restricted the subsequent use of the buildings despite the main frames having sustained no more than minor structural damage. Partial or complete out-of-plane (OOP) collapse of masonry infills has also been frequently observed following large earthquakes, often causing collateral damage to surrounding properties and injuries to passers-by. Despite these concerns, limited literature exists on the residual OOP strength of in-plane (IP) damaged infill walls, particularly those that have been strengthened using fibre reinforced matrix (FRCM) prior to the earthquake. Therefore, an experimental program was undertaken to evaluate the residual OOP capacity of IP damaged FRCM strengthened infill walls constructed using un-grouted unreinforced hollow core concrete masonry. A total of eight single bay RCFMI assemblies were constructed, including one non-retrofitted control specimen and with the remainder strengthened by applying diagonally oriented FRCM bands with varying widths onto both wall faces. The variables investigated were FRCM type and width of the applied FRCM band. The RCFMI assemblies were subjected to reversed cyclic displacement-controlled IP loading gradually increasing to 1% storey drift, to develop damage that would be expected from a moderate earthquake. The IP damaged RCFMI assemblies were then subjected to gradually increasing OOP loading to assess their residual capacity. Performance metrics that were observed and measured included observed damage patterns, failure mechanisms, force-displacement response, displacement ductility, and stiffness characteristics.