Few active galactic nuclei (AGN) reveal double-sided jet systems. However, these systems are crucial to understand basic physical properties of extragalactic jets. We address the questions whether jets in AGN are symmetric in nature, how well they are collimated on small scales, and how they evolve with time. We monitored the sub-parsec scale morphology of NGC 1052 with the Very Long Baseline Array at 43GHz from 2005 to 2009. A detailed study of 29 epochs show a remarkable asymmetry between both jets. A kinematic analysis of the outflows reveals higher apparent velocities for the eastern (approaching) jet as compared to the western (receding) jet, i.e., {beta}_ej_=0.529+/-0.038 and {beta}_wj_=0.343+/-0.037, respectively. Contradictory to previous studies, we find higher flux densities for the western jet as compared to the eastern. The distribution of brightness temperature and jet width features well-collimated jets up to 1 mas distance to the dynamic center and a nearly conical outflow further outward. By combining flux density ratios and velocities of the jet flows, we were unable to find a combination of intrinsic velocities and inclination angles of the jets that is consistent for all four years of observation; this contradicts findings for symmetrically evolving jets. Spectral index maps between quasi-simultaneous 22GHz and 43GHz observations support the existence of an optically thick absorber covering the innermost ~=1.6mas around the 43GHz central feature and an optically thin jet emission with a spectral index of <=-1. Our results fit into a picture in which we expect larger internal energy and/or magnetic flux in the western jet and higher kinetic energy in the eastern jet. Previous observations at lower frequencies have found slower velocities of the moving jet features as compared to this work. Considering the different velocities in different areas, we suggest a spine-sheath structure with a faster inner layer and slower outer layer.