  We prove the unconditional uniqueness of solutions to the derivative
nonlinear Schr\"odinger equation (DNLS) in an almost end-point regularity. To
this purpose, we employ the normal form method and we transform (a
gauge-equivalent) DNLS into a new equation (the so-called normal form equation)
for which nonlinear estimates can be easily established in $H^s(\mathbb{R})$,
$s>\frac12$, without appealing to an auxiliary function space. Also, we prove
that low-regularity solutions of DNLS satisfy the normal form equation and this
is done by means of estimates in the $H^{s-1}(\mathbb{R})$-norm.
