Thanks to their absence of play, absence of contact friction and possible monolithic fabrication, flexure pivots offer advantages over traditional bearings in small-scale, high accuracy applications and environments where lubrication and wear debris are proscribed. However, they typically present a so-called parasitic center shift that deteriorates their rotational guidance accuracy. Existing solutions addressing this issue have the drawbacks of reducing angular stroke, prohibiting planar design, or introducing overconstraints or underconstraints. This article introduces a new triple crossed flexure pivot called TRIVOT that has a reduced parasitic shift without overconstraints nor internal mobility while allowing either optimal stress distribution in the flexures or a planar design. The new architecture also makes it possible to place the center of rotation outside of the physical structure, which is not the case with traditional bearings. Based on finite element simulations, we show that the parasitic shift is reduced by one order of magnitude in comparison to the widely used crossed flexure pivot. We also derive and validate formulas for the rotational stiffness and angular stroke limit of the TRIVOT for given dimensions and material, which are valuable for its dimensioning towards practical applications. We expect this new pivot to become a competitive alternative to the crossed flexure pivot for applications where high accuracy and compactness are required.