Compared to the disordered HCP metals, the α2-Ti3Al phase is reluctant to twin due to its D019 ordered structure. Recently, abundant {202¯1} compression twins were observed in this phase. However, other type of twin has not been reported besides the {202¯1} ones. In this study, we observed the {11¯01} tension twins in the ordered α2-Ti3Al phase for the first time in the α2+γ two phase TiAl alloy. In addition, the {11¯01}<1¯102> tensile mode occurs together with {202¯1}<1¯014> compression twins already known for the α2 phase, and these two modes are often twinned internally. Two types of double twins ({11¯01}-{22¯01} and {22¯01}-{11¯01}) were observed. The structure of the various interfaces was examined with high-resolution electron microscopy. The factors governing the evolution of the observed twin architecture are discussed with particular emphasis on deformation induced internal stresses and the interchange shuffles necessary to restore the D019 ordering of the α2 phase in its twinned counterpart. The transformation matrix was calculated for the observed two types of double twin structures, which explains the reorientation of the grains and the shear continuity, further confirming the double twin mechanism. The variant selection mechanism of the secondary twin is also discussed. These results indicate that abundant twinning activity can be initiated in the ordered α2 phase under severe deformation.