A systematic method for the conversion of first class constraints to a
n equivalent set of the Abelian constraints based on the Dirac equival
ence transformation is developed. A representation for the correspondi
ng matrix of this transformation is proposed. This representation allo
ws one to reduce the problem of Abelianization to the solution of a ce
rtain system of first order linear differential equations for matrix e
lements. (C) 1996 American Institute of Physics.