Since quasicrystals provide additional freedom to expand photonic bandgap, dielectric quasi-periodic sequences of broadbands become crucial for implementing low-loss omnidirectional reflectors or filters. The current major challenge is to find an elegant scheme to construct angle-insensitive multilayer structures with fewer layer numbers. In this work, we create an appealing quasiperiodic ordering of the dielectric-reversal Fibonacci sequence to optimize the properties of omnidirectional reflectors. We have concatenated it to a periodic sequence to construct the omnidirectional reflector of hybrid multilayers with thin thickness and reflectivity above 99% over a visible scope from 436 nm to 559 nm. An ultrabroad polarization-independent omnidirectional bandgap of the relative bandwidth of 39.8% has been achieved by cascading two dielectric-reversal ordering sequences. The self-similarity of Fibonacci multilayer structures along with this characteristic quasiperiodic order guarantees the existence of perfect omnidirectional reflections at any scale. This ordering strategy of dielectric-reverse essentially differs from previous conjugate and recursion methods, which will significantly enrich the variety of quasiperiodic orders in theory and applied science domains.