  Since the last phase coherent timing solution of the nearby radio-quiet
isolated neutron star RX J0720.4-3125 six new XMM-Newton and three Chandra
observations were carried out. The phase coherent timing solutions from
previous authors were performed without restricting to a fixed energy band.
However, we recently showed that the phase residuals are energy dependent, and
thus phase coherent solutions must be computed referring always to the same
energy band. We updated the phase coherent timing solution for RX J0720.4-3125
by including the recent XMM-Newton EPIC-pn, MOS1, MOS2 and Chandra ACIS data in
the energy range 400-1000~eV. Altogether these observations cover a time span
of almost 10~yrs. A further timing solution was obtained including the ROSAT
pointed data. In this case, observations cover a time span of $\approx$16~yrs.
To illustrate the timing differences between the soft band (120-400~eV) and the
hard band (400-1000~eV) a timing solution for the soft band is also presented
and the results are verified using a $\mathrm{Z_{n}^{2}}$ test. In contrast to
previous work, we obtain almost identical solutions whether or not we include
the ROSAT or Chandra data. Thanks to the restriction to the hard band, the data
points from EPIC-pn are in better agreement with those from MOS1, MOS2 and
Chandra than in previous works. In general the phase residuals are still large
and vary with time. In particular, the latest XMM-Newton and Chandra data show
that the phase residuals have attained relatively large and negative values.
