  A detailed analysis of the BF formulation for general relativity given by
Capovilla, Montesinos, Prieto, and Rojas is performed. The action principle of
this formulation is written in an equivalent form by doing a transformation of
the fields of which the action depends functionally on. The transformed action
principle involves two BF terms and the two Lorentz invariants that appear in
the original action principle generically. As an application of this formalism,
the action principle used by Engle, Pereira, and Rovelli in their spin foam
model for gravity is recovered and the coupling of the cosmological constant in
such a formulation is obtained.
