  A new transformation $u=4 ({\rm ln}f)_x$ that can formulate a quintic linear
equation and a pair of Hirota's bilinear equations for the (2+1)-dimensional
Sawada-Kotera (2DSK) equation is reported firstly, which enables one to obtain
a new hierarchy of multiple soliton solutions of the 2DSK equation. It tells a
crucial fact that a nonlinear partial differential equation could possess two
hierarchies of multiple soliton solutions and the 2DSK equation is the first
and only one found in this paper. The quintic linear equation is solved by a
pair of Hirota's bilinear equations, of which one is the (2+1)-dimensional
bilinear SK equation obtained by $u=2 ({\rm ln}f)_{x}$, and the other is the
bilinear KdV equation. The (1+1)-dimensional SK equation does not possess this
property. As another example, a (3+1)-dimensional nonlinear partial
differential equation possessing a pair of Hirota's bilinear equations, however
only bearing one hierarchy of multiple soliton solutions is studied.
