The paper aims at developing the Bayesian seasonally cointegrated model for quarterly data. We propose the prior structure, derive the set of full conditional posterior distributions, and propose the sampling scheme. The identification of cointegrating spaces is obtained \emph{via} orthonormality restrictions imposed on vectors spanning them. In the case of annual frequency, the cointegrating vectors are complex, which should be taken into account when identifying them. The point estimation of the cointegrating spaces is also discussed. The presented methods are illustrated by a simulation experiment and are employed in the analysis of money and prices in the Polish economy.