Magnetic properties of Fe/NiO bilayers grown on a (1,1,10) vicinal surface of Ag(001) were studied by magneto-optical Kerr effect (MOKE) and x-ray magnetic linear dichroism (XMLD). The orientation of the antiferromagnetically (AFM) aligned spins of NiO films shows an in-plane spin-reorientation transition (SRT) from parallel to perpendicular to the steps with increasing NiO thickness. Two in-plane SRTs of Fe moments are found in dependence of the NiO thickness. The first SRT of the Fe magnetization from parallel to perpendicular to the steps is observed at NiO thickness where antiferromagnetic order is found, the second at the NiO thickness of the SRT in the NiO film. Also, the in-plane SRT of Fe spins driven by a temperature increase is observed. The perpendicular coupling between the Fe and NiO spins is proven. The induced uniaxial anisotropy energy is estimated to be 0.12 erg/cm².