An explanation of the mystery of the extended 23rd solar cycle duration about 13 years in the frame of non-linear regime of the αΩ- dynamo model is proposed. The calculated dynamo-period of the solar cycle, T, depends (in the inverse proportion) on the intensity of the α- effect in the solar convection zone (SCZ). As well, the intensity of the α- effect in non-linear regime depends (also in the inverse proportion) on the value of toroidal magnetic field, B T (magnetic alpha-quenching). Thus, the calculated period is in direct proportion to the value of toroidal magnetic field: the stronger toroidal field B T in certain cycle, the longer dynamo-period T of this cycle. Since the toroidal field is hidden in the deep layers of the SCZ, it is necessary to know some other magnetic experimental evidence that reflects something like information about inner toroidal field. In this connection we allow for that the strong toroidal field is transported by magnetic buoyancy to the solar surface and produces here the sunspots, so they carry indirect information on B T . In this connection we took into account up-to-date observed data on the essential increase of the averaged annual module of the magnetic field of the large-scale sunspots, B sp , in the 23rd cycle; and then we made calculation of the alpha-quenching which depends on these referred data. It is important to know only relative variations of magnetic index B sp for calculation of the dynamo-period variation. Our estimations showed that the average solar period, which is about 11 years, must increase by a factor of 1,2; so the calculated 23rd cycle dynamo-period would be about 13 years.