We describe a search method for fast moving (beta = v/c > 5 x 10(-3)) magnetic monopoles using simultaneously the scintillator, streamer tube and track-etch subdetectors of the MACRO apparatus. The first two subdetectors are used primarily for the identification of candidates while the track-etch one is used as the final tool for their rejection or confirmation. Using this technique, a first sample of more than two-years of data has been analyzed without any evidence of a magnetic monopole. We set a 90% CL upper limit to the local monopole flux of 1.5 x 10(-15) cm(-2) s(-1) sr(-1) in the velocity range 5 x 10(-3) less than or equal to beta less than or equal to 0.99 and for nucleon decay catalysis cross-section smaller than similar to1 mb (C) 2002 Elsevier Science B.V. All rights reserved.