This paper presents multiband photometric follow-up observations of the Neptune-mass transiting planet GJ 436b, consisting of five new ground-based transit light curves obtained in 2007 May. Together with one already published light curve, we have at hand a total of six light curves, spanning 29 days. The analysis of the data yields an orbital period P=2.64386+/-0.00003 days, midtransit time T_c_[HJD]=2454235.8355+/-0.0001, planet mass M_p_=23.1+/-0.9M_{earth}_=0.073+/-0.003M_Jup_, planet radius R_p_=4.2+/-0.2R_{earth}_=0.37+/-0.01R_Jup_, and stellar radius R_s_=0.45+/-0.02R_{sun}_. Our typical precision for the midtransit timing for each transit is about 30s. We searched the data for a possible signature of a second planet in the system through transit timing variations (TTV) and variation of the impact parameter. The analysis could not rule out a small, of the order of a minute, TTV and a long-term modulation of the impact parameter, of the order of +0.2yr^-1^.