An unexpected three-stage melting transition has been observed in two-dimensional (2D) free-standing liquid-crystal films by in situ electron-diffraction and optical-reflectivity measurements. These data suggest the existence of two phases between the 2D solid and liquid: a hexatic phase and, at a higher temperature, an intermediate liquid phase with hexatic-like positional correlations ( approximately 40 angstroms) but no long-range orientational order. Previous high-resolution heat-capacity measurements have revealed a divergent-like anomaly at the hexatic-liquid transition that sharply contradicts the predictions of 2D melting theories. The observation of an intermediate isotropic phase may alter our understanding of 2D melting and lead to reconciliation between current experiments and theories.