An equation describing the evolution of 2-D inhomogeneous magnetized plasma has been derived. In the cold ion case, it is merely a Euler equation or convective cell equation. There is a solitary flute vortex solution to it. Moreover, the structure of the solution is similar to that of the oblique vortex solution obtained by Makio et al. (1981) and Meiss and Horton (1982, 1983), but its properties differ from the latter in several aspects. There is no restriction on the speed of the vortex and it can propagate in any direction in a plane with magnetic field B as it is normal, although the effect of a warm ion makes the vortices propagate anisotropically in the plane. The plasma appears to be adhered to vortices and moving along with them. This means that the existence of flute vortices could be connected with convection of particles and energy of plasma across magnetic surfaces.