In this letter we discuss a new entanglement measure. It is based on the Hi
lbert-Schmidt norm of operators, We give an explicit formula for calculatin
g the entanglement of a large set of states on C-2 X C-2. Furthermore we fi
nd some relations between the entanglement of relative entropy and the Hilb
ert-Schmidt entanglement. A rigorous definition of partial transposition is
given in the Appendix. (C) 1999 Published by Elsevier Science B.V. All rig
hts reserved.