  We propose a discrete non-abelian symmetry group which enforces maximal
atmospheric neutrino mixing, while $\theta_{13} = 0$ and the solar mixing angle
$\theta_{12}$ remains undetermined; without finetuning, $\theta_{12}$ will be
large but non-maximal. Our extension of the Standard Model has three
right-handed neutrino singlets $\nu_R$ and implements the seesaw mechanism.
Furthermore, we have an enlarged scalar sector with three Higgs doublets and
two scalar gauge singlets; the latter have masses and vacuum expectation values
of the order of the seesaw scale. Lepton mixing stems exclusively from the
$\nu_R$ Majorana mass matrix, where non-diagonal elements are generated by the
vacuum expectation values of the scalar singlets. The model predicts a neutrino
mass spectrum with $m_3 > m_2 > m_1$ and the effective Majorana mass of
neutrinoless $\beta\beta$ decay is equal to $m_1 m_2 / m_3$.
