  We provide a systematic and thorough exploration of the $\Delta(48)$ family
symmetry and the consistent generalised CP symmetry. A model-independent
analysis of the achievable lepton flavor mixing is performed by considering all
the possible remnant symmetries in the neutrino and the charged lepton sectors.
We find a new interesting mixing pattern in which both lepton mixing angles and
CP phases are nontrivial functions of a single parameter $\theta$. The value of
$\theta$ can be fixed by the measured reactor mixing angle $\theta_{13}$, and
the excellent agreement with the present data can be achieved. A supersymmetric
model based on $\Delta(48)$ family symmetry and generalised CP symmetry is
constructed, and this new mixing pattern is exactly reproduced.
