  It is shown that extreme problem for one-dimensional Euler-Lagrange
variational functional in $C^1[a;b]$ under the strengthened Legendre condition
can be solved without using Hamilton-Jacobi equation. In this case, exactly one
of the two possible cases requires a restriction to a length of $[a;b]$,
defined only by the form of integrand. The result is extended to the case of
compact extremum in $H^1[a;b]$.
