  In this paper, we prove that the product of a paired calibrated set and a set
of codimension 1 calibrated by a coflat calibration with small singularity set
is Almgren minimal. This is motivated by the attempt to classify all possible
singularities for Almgren minimal sets--Plateau's problem in the setting of
sets. In particular, a direct application of the above result leads to various
types of new singularities for Almgren minimal sets, e.g. the product of any
paired calibrated cone (such as the cone over the $d-2$ skeleton of the unit
cube in $\R^d, d\ge 4$) with homogeneous area minimizing hypercones (such as
the Simons cone).
