The NGC 1333 region was observed in the H₂ 1-0 S(1) line. The H₂ images cover a 5' × 7' region around IRAS 4. Numerous H₂ emission features were detected. The northeast-southwest bipolar outflow driven by IRAS 4A was studied by combining the H₂ images with SiO maps published previously. The SiO-H₂ outflows are continuous on the southwestern side but show a gap on the northeastern side. The southwestern outflow lobe curves smoothly, and the position angle increases with the distance from the driving source. The base and the outer tip of the northeastern outflow lobe are located at positions opposite to the corresponding parts of the southwestern lobe. This point symmetry suggests that the outflow axis may be drifting or precessing clockwise in the plane of the sky and that the cause of the axis drift may be intrinsic to the outflow engine. The axis drift model is supported by the asymmetric lateral intensity profile of the SiO outflow. The axis drift rate is ~0011 yr^-1. The middle part of the northeastern outflow does not exactly follow the point symmetry because of the superposition of two different kinds of directional variability: the axis drift of the driving source and the deflection by a dense core. The axis drift model provides a good explanation for the large deflection angle of the northeastern outflow. Other H₂ emission features around the IRAS 4 region are discussed briefly. Some of them are newly found outflows, and some are associated with outflows already known before.