A corrugated spline-profile horn has been designed to meet the stringent specifications and constraints of a receiver for Band 1 (31.3-45 GHz) of the Atacama Large Millimeter Array (ALMA). Given the physical restrictions of the receiver, the horn will be located behind a focusing lens placed 191 mm over its aperture. After this first focusing stage, the horn must have a reflection coefficient less than -20 dB and the cross-polarization not exceeding the -30 dB level in the entire frequency range. The side-lobes should be less than -25 dB at all frequencies and its half power beamwidth must be approximately 24A degrees at 31.3 GHz and 16A degrees at 45 GHz. The horn has been constructed using the split-block technique and characterized in a near-field scanner setup. The results show an excellent performance complying with all the requirements.