We present and discuss current waveforms associated with 13 bipolar lightning flashes recorded at the Säntis Tower during the period from June 2010 to January 2015. During this period, a total of 427 flashes were recorded, of which 13 (3%) were classified as bipolar flashes. The majority of the recorded flashes (10 out of 13) exhibited a polarity reversal during the initial continuous current, therefore belonging to Category I according to the classification proposed by Rakov (2003). Of the three remaining flashes, two were characterized by different polarities of the initial stage current and the following return stroke or strokes (Category II), and one flash involved return strokes of opposite polarity within the same flash (Category III). In Category I bipolar flashes, the polarity reversal is usually assumed to be associated with in-cloud processes. However, two of our 10 Category I flashes appeared to be each a sequence of two upward discharges of opposite polarity, initiated from the tower within tens of milliseconds of each other. This is the first time that such a sequence has been observed from the same tower. We suggest that the traditional classification of bipolar flashes should be modified to distinguish between two types of Category I flashes: those in which the polarity reversal during the initial stage is associated with in-cloud processes (Category Ia) and those in which the polarity reversal is due to initiation of two opposite-polarity leaders from the tower (Category Ib).