  We present a novel technique for fitting restframe I-band light curves on a
data set of 42 Type Ia supernovae (SNe Ia). Using the result of the fit, we
construct a Hubble diagram with 26 SNe from the subset at 0.01< z<0.1. Adding
two SNe at z~0.5 yields results consistent with a flat
Lambda-dominated``concordance universe''
($\Omega_M,\Omega_\Lambda$)=(0.25,0.75). For one of these, SN 2000fr, new near
infrared data are presented. The high redshift supernova NIR data are also used
to test for systematic effects in the use of SNe Ia as distance estimators. A
flat, Lambda=0, universe where the faintness of supernovae at z~0.5 is due to
grey dust homogeneously distributed in the intergalactic medium is disfavoured
based on the high-z Hubble diagram using this small data-set. However, the
uncertainties are large and no firm conclusion may be drawn. We explore the
possibility of setting limits on intergalactic dust based on B-I and B-V colour
measurements, and conclude that about 20 well measured SNe are needed to give
statistically significant results. We also show that the high redshift
restframe I-band data points are better fit by light curve templates that show
a prominent second peak, suggesting that they are not intrinsically
underluminous.
