Absolute photonic band gaps (PBG's) can be substantially improved in two-dimensional (2D) lattices by rotating noncircular air rods in dielectric background, in which the configuration of high-dielectric regions that are both practically isolated and linked by narrow veins can be freely adjusted to create large absolute PBG's. For square lattice, the largest absolute PBG's in the single-square-rod and double-hybrid-rods structures are 315 and 150% sizes of those in the corresponding single-circular-rod and double-circular-rods structures, respectively. Furthermore, the large absolute PBG's persist in a wide range of filling fractions and reach their maxima far away from the close-packed conditions, and this is in vast favor of preparation of crystals. Such an approach is also applicable to other 2D lattices. It may open up a scope for engineering PBG’s.