We present and evaluate theoretically and experimentally a design for a negative-index metamaterial that is termed the "Swiss cross" structure. Compared with the established fishnet structure, the proposed design eliminates the drawback of polarization-dependent effective optical parameters. The new design is fabricated by means of e-beam technology and experimentally analyzed using spectroscopic techniques. The thorough comparison with numerical simulations reveals an effective refractive index of n=-1.9 at an operational wavelength of 1400 nm that is independent of the incident polarization. The resonances of the system are comprehensively discussed.