In this paper, extending past works of Del Popolo, we show how a high precision mass function (MF) can be obtained using the excursion set approach and an improved barrier taking implicitly into account a non-zero cosmological constant, the angular momentum acquired by tidal interaction of proto-structures and dynamical friction. In the case of the ΛCDM paradigm, we find that our MF is in agreement at the 3% level to Klypin's Bolshoi simulation, in the mass range M_vir = 5 × 10⁹ h⁻¹M_⊙–−5 × 10¹⁴ h⁻¹M^⊙ and redshift range 0≲z≲10. For z=0 we also compared our MF to several fitting formulae, and found in particular agreement with Bhattacharya's within 3% in the mass range 10¹²–10¹⁶ h⁻¹M_⊙. Moreover, we discuss our MF validity for different cosmologies.