  We re-visit the minimal area condition of Ryu-Takayanagi in the holographic
calculation of the entanglement entropy. In particular, the Legendre test and
the Jacobi test. The necessary condition for the weak minimality is checked via
Legendre test and its sufficient nature via Jacobi test. We show for AdS black
hole with a strip type entangling region that it is this minimality condition
that makes the hypersurface not to cross the horizon, which is in agreement
with that studied earlier by {\it Engelhardt et al.} and {\it Hubeny} using a
different approach. Moreover, demanding the weak minimality condition on the
entanglement entropy functional with the higher derivative term puts a
constraint on the Gauss-Bonnet coupling: that is there should be an upper bound
on the value of the coupling, $\lambda_a< \f{(d-3)}{4(d-1)}$.
