We will present a new approach to the treatment of equality constraints in the code PENNON. The code, designed to solve nonlinear optimization problems as well as semidefinite programs, is based on thegeneralized augmented Lagrangian algorithm. The original algorithm, due to R.~Polyak and Ben-Tal/Zibulevsky, was designed for problems with inequality constraints. The equality constraints were either treated by classic augmented Lagrangian approach or by rewriting an equality as two inequalities. Neither of these approaches was truly satisfying and the presence of equality constraints sometimes disqualified the code, otherwise very efficient for inequality constraints. We propose a new (within our framework)approach to equality constraints. Numerical tests will demonstrate its superiority the the currenly used ones.