On 29 December 2004 the Double Star TC-1 satellite most probably stays close to a reconnection line for about 20 min. The direction of the X line can be evaluated according to the component merging model. During the time of observations, TC-1 also detects a flux transfer event (FTE). It is found that the FTE axis is parallel to such an X line. This observation is more in favor of the single X line and the multiple X lines FTE models, rather than the original Russell and Elphic model. Moreover, particular features of the ion distribution functions and the plasma behavior near the FTE seem to be more consistent with a multiple X line generation mechanism. The period under study is characterized by a large and negative Earth's dipole tilt, and the reconnection line close to TC-1 is found to follow the magnetic equator, passing northward of the subsolar/stagnation point. These facts lead to speculate that the FTE is generated when a secondary X line, probably passing through the subsolar/stagnation point and with approximately the same orientation of the X line near TC-1, is activated southward of TC-1.