  We give a quick method of constructing strong homotopy associative algebra,
namely, the higher derived product construction. This method is associative
analogue of classical higher derived bracket construction in the category of
Loday algebras. We introduce a new type of algebra "Loday pair" which is
noncommutative analogue of classical Leibniz pair. We study strong homotopy
Loday pairs and the higher derived brackets on the Loday pairs.
