A thus far unknown phase of 1,4,5,8-naphthalene-tetracarboxylic dianhydride (NTCDA) on Ag(111), characterized by an all perpendicular orientation of the planar molecules and bound to the Ag substrate through the carboxyl oxygen atoms has been identified using infrared absorption spectroscopy and scanning tunneling microscopy. Its formation process requires second layer NTCDA to squeeze into empty spaces between relaxed monolayer NTCDA molecules. Remarkably, this process causes initially parallel oriented NTCDA to likewise adopt the new, highly inclined adsorption geometry. According to our SPA-LEED and STM findings, the new phase displays a distinct long range order and shows a pronounced tendency to form 1D rows or narrow islands. We suggest that extra NTCDA preferentially transforms into the upright configuration close to existing islands and attaches to them, i.e. the transformation process proceeds in a directed and recurrent manner (reverse domino scenario). Identical processing starting with a compressed NTCDA/Ag(111) monolayer leads to a purely parallel oriented bilayer, that is, the NTCDA monolayer phase is retained and merely acts as a passive template for bilayer NTCDA. The new vertical NTCDA phase represents an unusual molecular system with π–orbitals oriented parallel to a metal surface. A substantially reduced coupling of these orbitals to Ag(111) electronic levels is conjectured, which will have a major impact on intermolecular couplings and electronically excited state lifetimes.