  The renormalization group approach in three dimensions is used to estimate
the universal critical value g_6^* of the dimensionless sextic effective
coupling constant for the Ising model. The four-loop RG expansion for g_6 is
calculated and resummed by means of the Pade-Borel and Pade-Borel-Leroy
procedures resulting in g_6^* = 1.596, while the most accurate estimate for
g_6^* is argued to be equal to 1.61.
