Cholesteric liquid-crystalline states of matter are abundant in nature: atherosclerosis(1), arthropod cuticles(2,3), condensed phases of DNA(4), plant cell walls(2,5), human compact bone osteon6, and chiral biopolymers(7-10). The self-organized helical structure produces unique optical properties(11). Light is reflected when the wavelength matches the pitch (twice periodicity); cholesteric liquid crystals are not only coloured filters, but also reflectors and polarizers. But, in theory, the reflectance is limited to 50% of the ambient (unpolarized) light because circularly polarized light of the same handedness as the helix is reflected. Here we give details of a cholesteric medium for which the reflectance limit is exceeded. Photopolymerizable monomers are introduced into a cholesteric medium exhibiting a thermally induced helicity inversion, and the blend is then cured with ultraviolet light when the helix is right-handed. Because of memory effects attributable to the polymer network, the reflectance exceeds 50% when measured at the temperature assigned for a cholesteric helix with the same pitch but a left-handed sense before the reaction. As cholesteric materials are used as tunable bandpass filters, reflectors or polarizers and temperature or pressure sensors12, novel opportunities to modulate the reflection over the whole light flux range, instead of only 50%, are offered.