  We report on H-band, ground-based observations of a transit of the hot
Neptune GJ 436b. Once combined to achieve sampling equivalent to archived
observations taken with Spitzer, our measurements reach comparable precision
levels. We analyze both sets of observations in a consistent way, and measure
the rate of orbital inclination change to be of 0.02+/-0.04 degrees in the time
span between the two observations (253.8 d, corresponding to 0.03+/-0.05
degrees/yr if extrapolated). This rate allows us to put limits on the relative
inclination between the two planets by performing simulations of planetary
systems, including a second planet, GJ 436c, whose presence has been recently
suggested (Ribas et al. 2008). The allowed inclinations for a 5 M_E super-Earth
GJ 436c in a 5.2 d orbit are within ~7 degrees of the one of GJ 436b; for
larger differences the observed inclination change can be reproduced only
during short sections (<50%) of the orbital evolution of the system. The
measured times of three transit centers of the system do not show any departure
from linear ephemeris, a result that is only reproduced in <1% of the simulated
orbits. Put together, these results argue against the proposed planet candidate
GJ 436c.
