The Jones polynomial of a closed braid may be obtained from

a representation of the Temperley-Lieb algebra.

We define a new algebra by a modification of the definition

of the Temperley-Lieb algebra.

We show that the Alexander-Conway polynomial may be obtained

from a representation of this algebra.

Furthermore we introduce a bracket polynomial for the

Alexander-Conway polynomial and investigate it.

We obtain a construction of the Alexander-Conway polynomial

through a smoothing decomposition.