  We present a new 1/8 supersymmetric intersecting M-brane solution of D=11
supergravity with two independent rotation parameters. The metric has a
non-singular event horizon and the near-horizon geometry is $adS_3\times
S^3\times S^3\times\bE^2$ (just as in the non-rotating case). We also present a
method of determining the isometry supergroup of supergravity solutions from
the Killing spinors and use it to show that for the near horizon solution it is
$D(2|1,\alpha)\times D(2|1,\alpha)$ where $\alpha$ is the ratio of the two
3-sphere radii. We also consider various dimensional reductions of our
solution, and the corresponding effect of these reductions on the Killing
spinors and the isometry supergroups.
