We have recently suggested that one solar cycle was lost in the beginning of the Dalton minimum during 1790s <Usoskin et al., 2001>. Earlier, this cycle has been combined with the preceding activity to form the exceptionally long solar cycle 4 in 1784-1799 with an irregular phase evolution. Here we show that historical data of auroral occurrence provide independent evidence for the existence of the new cycle. Using a heliospheric model we demonstrate that 10Be or any other cosmogenic isotope data do not exclude the possibility of a new cycle. We also discuss the other implications of the new cycle for solar activity, in particular the cycle length distribution and the Waldmeier relation between the cycle amplitude and the length of the ascending and descending phase. Including the new cycle also restores the Gnevyshev-Ohl rule of cycle pairing and removes the phase catastrophe in the beginning of the Dalton minimum.