It is well established numerically that spectral statistics of pseudo-integrable models differs considerably from the reference statistics of integrable and chaotic systems. In Bogomolny and Schmit (2004 Phys. Rev. Lett. 93 254102) statistical properties of a certain quantized pseudo-integrable map had been calculated analytically but only for a special sequence of matrix dimensions. The purpose of this paper is to obtain the spectral statistics of the same quantum map for all matrix dimensions.