  A lattice in the Euclidean space is standard if it has a basis consisting
vectors whose norms equal to the length in its successive minima. In this
paper, it is shown that with the $L^2$ norm all lattices of dimension $n$ are
standard if and only if $n\leqslant 4$. It is also proved that with an
arbitrary norm, every lattice of dimensions 1 and 2 is standard. An example of
non-standard lattice of dimension $n\geqslant 3$ is given when the lattice is
with the $L^1$ norm.
