Summary Passive tuned mass dampers (TMDs) are widely used in controlling structural vibrations. Although their principle is well established, the search for improved arrangements is still under way. This effort has recently produced an innovative paradigm of bidirectional pendulum TMD (BTMD) that, moving along a specially designed three‐dimensional (3D) surface, can simultaneously control two in‐plane orthogonal structural modes. In existing versions of BTMDs, energy dissipation is provided either by ordinary horizontal viscous dampers or by an original arrangement of vertical friction dampers. In this paper, a new paradigm is proposed, in which energy dissipation comes from the tangential friction arising along the pendulum surface out of an optimal spatially variable friction coefficient pattern. Within this paradigm, if the friction coefficient is taken proportional to the modulus of the pendulum surface gradient, the dissipation model results nonlinear homogeneous in the small‐displacement domain, and the performance of the absorber, herein called the homogeneous tangential friction BTMD (HT‐BTMD), results independent from the excitation level. The present work introduces this concept, derives the analytical model of the HT‐BTMD, establishes a method for its optimal design, and numerically verifies its seismic effectiveness in comparison with viscously damped devices. The validity and feasibility of the concept are demonstrated through experimental tests on a small‐scale lab prototype, which also show the efficacy of a stepwise approximation of the homogeneous friction pattern. The new device proves a competing alternative to existing BTMDs, and homogeneous tangential friction proves a promising new paradigm to provide pendular systems with amplitude‐independent structural damping.