Stability of the laminar boundary layer on the surface of a hypersonic nozzle for the Mach number M = 6 of the Transit-M wind tunnel is calculated. The laminar boundary-layer profiles are obtained by solving the Navier-Stokes equations numerically within the framework of the Ansys Fluent software. N-factors of the Goertler vortices and of the first and second Mack modes are obtained in the approximation of the linear stability theory. It is demonstrated that the Goertler vortices are the most unstable disturbances for the nozzle under consideration. Empirical dependences of the local Reynolds number of the laminar-turbulent transition on the N-factor and unit Reynolds number are determined.