The Navier-Stokes equations admit symmetry properties, such as the two-dimensional material indifference [10], the invariance under the generalized Galilean transformation, under constant rotations or under certain scaling transformations [4]. These properties are fundamental for the understanding of fluid mechanics and, in particular, of turbulence. For example, they can be used for the derivation of conservation laws (Noether's theorem [5]). Oberlack used the symmetry method to obtain turbulent scaling laws from the Navier-Stokes equations [7]. Further, symmetries enable to calculate analytical (self-similar) solutions ([2]). Some self-similar solutions are particularly important because they represent interesting physical solutions (for example, a vortex solution [3]) or an asymptotic behavior of the flow [1]. The introduction of turbulence models into the filtered Navier-Stokes equations may destroy the symmetry properties and, by this way, the physical properties contained in the original equations of motion. In addition, it has been shown by Oberlack in [6] and by Razafindralandy and Hamdouni in [8] that only a few subgrid models in the literature are compatible with the symmetries of the Navier-Stokes equations. At the same time, many existing turbulence models, such as the popular dynamic model, are not conform with the second law of thermodynamics because they may induce negative dissi-pation. Presently, we propose to build a new class of subgrid models which preserve the symmetries of the equations and which, moreover, are consistent with the second law of thermodynamics. In order to have models preserving the translational and rotational symmetry properties of the Navier-Stokes equations, the subgrid stress tensor τ s is taken to be a function of the filtered strain rate tensor S, the subgrid-scale energy q and the dissipation rate ε. Tensor invariance theory leads to the following form of τ s :