A numerical Positive Definite Pseudo-Spectral (PDPS) method for the solution of the advection equation is presented. The method consists of two parts. For each time step first a solution using a pseudospectral method is computed. Then the solution is corrected by a filtering procedure which eliminates negative values. The numerical test with the rotational velocity field and different initial conditions shows that the present method has the accuracy of the pseudospectral one without producing negative values. An additional advantage of the PDPS method is the elimination of spurious artificial shortwaves typical for the pseudospectral solution
