By introducing trigonometric functions, a 2D hyperchaotic map with conditional symmetric attractors is constructed, where a symmetric pair of hyperchaotic attractors and asymmetric hyperchaotic attractors is found. For the existence of periodic feedback, the newly proposed map also exhibits attractor growth under specific circumstances. The polarity balance of the discrete map can be restored from the applied sinusoidal functions, combined with an extra inversion of the constant term. To the best of our knowledge, the above properties are not found in other chaotic maps. Finally, the hardware implementation based on STM32 is conducted, and the corresponding results agree with the numerical simulation and the theoretical analysis.