  The X-ray thermal isolated neutron star (XTINS) RX J0806.4--4123 shows
interesting multiwavelength properties that seemingly deviate from those of
similar neutron stars. An accurate determination of the spin frequency change
over time can assist in interpreting RX J0806.4-4123's properties in comparison
to those of other XTINSs and the wider pulsar population. From 2019 to 2023 we
carried out a tailored X-ray timing campaign of RX J0806.4-4123 with the NICER
instrument. We used statistical properties of the Fourier coefficients and the
$Z_K^2$ test for phase-connecting separate observations and finding a timing
solution for the entire dataset. We also developed a simple and universal
method for estimating the uncertainties of frequency $\nu$ and its derivative
$\dot{\nu}$ from the empirical dependencies of $Z_K^2$ on trial values of these
parameters, with account of all significant harmonics of the frequency.
Applying this method, we determined a spin-down rate $\dot{\nu} =
-7.3(1.2)\times 10^{-17}\,{\rm Hz\, s}^{-1}$. The resulting spin-down power
$\dot{E}=2.6\times 10^{29}$ erg s$^{-1}$ is the lowest among the XTINSs, and it
is a factor of 60 lower than the X-ray luminosity of this neutron star. RX
J0806.4-4123 is also among the pulsars with the lowest measured $\dot{E}$ in
general.
