Follows an from previous papers by the authors, where TWONE, a method
for solving global optimization problems in two dimensions was present
ed. Presents an improved version. If Omega is a compact connect subset
of R-2 looks for the minimum of a function f defined on Omega with va
lues in R-2. TWONE method considers the restriction of f to an alpha a
-dense curve in R-2. That implies the resolution of a one dimensional
problem. Gives some alpha-dense curves in R-2 with alpha as small as w
e want. Has biomedical and biocybernetic implications.