  We generalize the Moishezon Teicher algorithm that was suggested for the
computation of the braid monodromy of an almost real curve. The new algorithm
suits a larger family of curves, and enables the computation of braid monodromy
not only of caspidal curves, but of general algebraic curves, with some non
simple singularities. Moreover, it works also when in the fiber the curve
admits any number of imaginary points. We also provide two examples of how to
use the generalized algorithm.
