  We introduce a two-parameters bt-algebra which, by specialization, becomes
the one-parameter bt-algebra, introduced by the authors, as well as another
one-parameter presentation of it; the invariant for links and tied links,
associated to this two-parameter algebra via Jones recipe, contains as
specializations the invariants obtained from these two presentations of the
bt-algebra and then is more powerful than each of them. Also, a new non
Homflypt polynomial invariant is obtained for links, which is related to the
linking matrix.
