Results. The stellar parameters derived for the cool star in Me 1-1 are T-eff=4500 K and log g=2.0, which correspond to a spectral type of K(1-2) II. This star is rapidly rotating with a projected rotational velocity of V-rot=90 km s(-1). Its estimated mass is 3.5 M-circle dot with a distance of 6 kpc and a luminosity of 370 L-circle dot. The cool star in Me 1-1 has nearly solar iron and calcium abundances. Barium, a monitor of s-process nucleo synthesis, is not enriched. We show that this cool star has reached the base of the RGB and its accreted matter has been diluted by the deepening convective envelope. The images strongly suggest that Me 1-1 is an edge-on ring with incipient bipolar lobes. The central star is displaced similar to 400 AU from the center of the nebula. The expansion velocity of the ring ranges from 10 and 13 km s(-1) in the different emission lines. Broad (600 km s(-1)) wings are detected in the Ha emission, probably with a stellar origin. A comparison of Me 1-1 with other ring-like planetary nebula shows that most of them host off-center binary central stars.