  In this article we prove that the union of two almost orthogonal planes in R4
is Almgren-minimal. This gives an example of a one parameter family of minimal
cones, which is a phenomenon that does not exist in R3. This work is motivated
by an attempt to classify the singularities of 2-dimensional Almgren-minimal
sets in R4. Note that the traditional methods for proving minimality
(calibrations and slicing arguments) do not apply here, we are obliged to use
some more complicated arguments such as a stopping time argument, harmonic
extensions, Federer-Fleming projections, etc. that are rarely used to prove
minimality (they are often used to prove regularity). The regularity results
for 2-dimensional Almgren minimal sets ([5],[6]) are also needed here.
