  We propose and discuss a new Littlest Seesaw model, realised in the
tri-direct CP approach, in which the couplings of the two right-handed
neutrinos to the lepton doublets are proportional to $(0,-1,1)$ and
$(1,5/2,-1/2)$ respectively with the relative phase $\eta=-\pi/2$. This model
can give an excellent description of lepton flavour mixing, including an
atmospheric neutrino mixing angle in the second octant, in terms of only two
input parameters. We show that the observed baryon asymmetry can be generated
for the lightest right-handed neutrino mass $M_{1}=1.176\times 10^{11}$ GeV in
SM and $M_{1}=3.992\times 10^{10}$ GeV in MSSM with $\tan\beta=5$. We construct
an explicit Littlest Seesaw model based on the flavour symmetry $S_4\times
Z_4\times Z_9$ in which the desired alignments and the phase $\eta=-\pi/2$ are
achieved.
