The high spin states of the neutron-rich odd-odd 106Tc nucleus have been reinvestigated by observing prompt γ-rays from the spontaneous fission of 252Cf. A previously known collective band is confirmed and expanded, and a new collective band is newly identified. Several levels in previous report in 106Tc are reexamined and they belong to the members of a band in 107Tc. The total Routhian surface (TRS) calculations show that the 106Tc has triaxial shape. The spins and parities as well as the configurations for these bands have been tentatively assigned according to the analysis of the angular momentum alignments.