We present new results of searches for neutrino point sources in the northern sky, using data recorded in 2007-2008 with 22 strings of the IceCube detector (approximately one-fourth of the planned total) and 275.7 days of live time. The final sample of 5114 neutrino candidate events agrees well with the expected background of atmospheric muon neutrinos and a small component of atmospheric muons. No evidence of a point source is found, with the most significant excess of events in the sky at 2.2 sigma after accounting for all trials. The average upper limit over the northern sky for point sources of muon-neutrinos with E-2 spectrum is E-2 Phi(v mu) < 1.4 x 10(-11) TeV cm(-2) s(-1), in the energy range from 3 TeV to 3 PeV, improving the previous best average upper limit by the AMANDA-II detector by a factor of 2.