A representation of a finite Larmor radius plasma is proposed, which permits the transition rL to infinity without becoming mathematical ill-posed. It is being used in a two-dimensional spectral plasma code in which both the ions and electrons are represented as guiding centers. The ion Larmor radius is subsequently averaged analytically for every Fourier mode. Finite Larmor radius densities and velocities are thus obtained from guiding center quantities by application of a filter in wave vector space. The numerical results show good agreement with experimental results on the coalescence of two convective cells.