A rectangular (3 x 2 radical3) surface lattice for long-term-annealed dodecanethiol self-assembled monolayers on Au(111) is observed by ultra-high-vacuum scanning tunneling microscopy. The new lattice has the same density and a unit cell of the same size as the well-known c(4 x 2) reconstruction. In contrast, it does not show hexagonal symmetry but rather a sort of thiol pairing, leading to a shift in the binding position of every second molecule. The described structure is believed to be an intermediate phase close to desorption.