This paper considers isometric
invariants of vectors in lattices (quadratic forms) over the ring of integers in a
local field for the prime 2. By extending the notion of order to vectors in
the lattice we obtain a set of invariants which enable the general vector to
be decomposed into a sum of simple vectors. The lengths of these simple
vectors are invariant modulo certain powers of 2 and these lengths together
with the original invariants form a complete set for the 2-adic integers. In
the special case where there are no one dimensional, orthogonal sublattices
(improper quadratic forms) the invariants form a complete set for all local
fields.
