  A new static partially twisted solution of N=4, SO(4) gauged supergravity in
D=11 is obtained in this work using Cveti\^c et al embedding of four
dimensional into eleven dimensional supergravities. In four dimensions we get
two solutions: an asymptotic one corresponding to $AdS_4$ and a near horizon
fixed point solution of the form $AdS_2\times H_2$. Hence, while the former
solution has 32 supercharges the latter turns out to have only 4 conserved.
Moreover, we managed to find an exact interpolating solution, thus connecting
the above two. Aiming at a future study of $AdS/CFT$ duality for the theory at
hand we derived the Penrose limit of the four dimensional solutions.
Interestingly the pp-wave limit of the near horizon solution suggests itself as
being of the supernumerary supersymmetric type. In D=11 we exhibit the uplift
of the four dimensional solutions: one associated to $AdS_4\times S^7$ and the
other to a foliation of $AdS_2\times H_2 \times S^7$, as well as their pp-wave
limits.
