  We present a precise timing analysis of the accreting millisecond pulsar XTE
J1814-338 during its 2003 outburst, observed by RXTE. A full orbital solution
is given for the first time; Doppler effects induced by the motion of the
source in the binary system were corrected, leading to a refined estimate of
the orbital period, P_orb=15388.7229(2)s, and of the projected semimajor axis,
a sini/c= 390.633(9) lt-ms. We could then investigate the spin behaviour of the
accreting compact object during the outburst. We report here a refined value of
the spin frequency (nu=314.35610879(1) Hz) and the first estimate of the spin
frequency derivative of this source while accreting (nu^dot=(-6.7 +/- 0.7)
10^(-14) Hz/s). This spin down behaviour arises when both the fundamental
frequency and the second harmonic are taken into consideration. We discuss this
in the context of the interaction between the disc and the quickly rotating
magnetosphere, at accretion rates sufficiently low to allow a threading of the
accretion disc in regions where the Keplerian velocity is slower than the
magnetosphere velocity. We also present indications of a jitter of the pulse
phases around the mean trend, which we argue results from movements of the
accreting hotspots in response to variations of the accretion rate.
