  The standard formalism of quantum mechanics is extended to describe a total
system including the reference system (RS), with respect to which the total
system is described. The RS is assumed to be able to act as a measuring
apparatus, with measurement records given by the values of some reference
properties of the RS. In order to describe the total system, we define a frame
of reference (FR) as a set of states that can be used to express all other
states of the total system. The theory is based on four basic postulates, which
have, loosely speaking, the following contents. (i) A reference property of a
RS has a definite value and is sufficiently stable in the FR directly related
to the reference property. (ii) States of the total system are associated with
vectors in the Hilbert space. (iii) Schr\"odinger equation is the dynamical law
in each valid FR. (iv) Under certain condition a property of a system can be
regarded as a reference property; vector descriptions of the total system given
in different FRs of the same RS may have a probabilistic relationship like in
Born's rule.
