Starting from an arbitrary codistributive element $a$ in an algebraic lattice $\mathcal L$, a new operation $*_a$ on the underlying set $L$ is defined. This operation determines an ordering relation on $L$. A properties of the new poset are investigated. Some necessary and some sufficient conditions under which it is a lattice are presented. An application of the results to the weak congruence lattice is given. A new characterization of the Congruence Extension Property (CEP) in terms of weak congruences under the new ordering is obtained.