The dynamics of the highly excited carbonyl sulfide molecule has been studied by means of a method of fast Lyapunov Indicators (FLI). We are dealing with the classical nonlinear model of the molecule.The method of the FLI is analogous to the finite Lyapunov exponent computations.Similar to the Poincaré picture we present the pictures of Lyapunov fields for energies below and at the dissociation threshold of the molecule. They show evolution of stability in the system with increase of the energy. By finding critical values of the fast Lyapunov indicators we can distinguish regular from chaotic motions and compute degree of regularity of the system for different energies. We perform a periodic orbit search confirming results of stability analysis.