We have measured time-of-flight (TOF) mass spectra of transition metal free clusters, TMn (TM=Fe, Ti, Zr, Nb, and Ta and n is the number of atoms per cluster), produced by a laser vaporization source. The size resolved TOF intensities at n=7, 13, 15 are much higher than those at the neighboring n values for all TMn. Such specific n values are assigned to the magic numbers of these transition metal clusters and can be related to pentagonal bipyramid, icosahedron, and bcc structure units. The other magic numbers are observed for larger TMn: n=19 and 23 for Fe, n=19 and 25 for Ti, being attributable to the polyicosahedron. The TOF spectra of Nb and Ta clusters are similar to each other and display the common magic number of n=22.