THz meta-foils have been introduced as an electromagnetic metamaterial, and their properties depend only on the geometric structure and the metal. Upon showing that conventional parallel-string meta-foils exhibit a strong polarization dependence, we propose and manufacture crossed meta-foils and demonstrate experimentally and numerically that their transmission spectra are polarization-independent. In this way, polarization-independent, all-metal, self-supported, free-standing, left-handed metamaterials are achieved, which provide a versatile platform for developing practical applications of metamaterials.