In contrast to polar cation displacements driving oxides into noncentrosymmetric and ferroelectric states, inversion-preserving anion displacements, such as rotations or tilts of oxygen octahedra about cation coordination centers, are exceedingly common. More than one nonpolar rotational mode in layered perovskites can lift inversion symmetry and combine to induce an electric polarization through a hybrid improper ferroelectric (HIF) mechanism. This form of ferroelectricity expands the compositional palette to new ferroelectric oxides because its activity derives from geometric rather than electronic origins. Here, the new Ruddlesden-Popper HIF Sr 3 Zr 2 O 7 , which is the first ternary lead-free zirconate ferroelectric, is reported and room-temperature polarization switching is demonstrated. This compound undergoes a first-order ferroelectric-to-paraelectric transition, involving an unusual change in the "sense" of octahedral rotation while the octahedral tilt remains unchanged. Our experimental and first-principles study shows that the paraelectric polymorph competes with the polar phase and emerges from a trilinear coupling of rotation and tilt modes interacting with an antipolar mode. This form of hybrid improper "antiferroelectricity" is recently predicted theoretically but has remained undetected. This work establishes the importance of understanding anharmonic interactions among lattice degrees of freedom, which is important for the discovery of new ferroelectrics and likely to influence the design of next-generation thermoelectrics.