  We present a new method based on Lie symmetries and Jacobi last multipliers
which allows one to find many non-standard Lagrangians for dissipative
dynamical systems. In particular, it is demonstrated that for every
non-standard Lagrangian one can generate a new non-standard Lagrangian
associated to a new equation of motion. We point out that the knowledge of Lie
symmetries for a given dynamical system generates Jacobi last multipliers which
can be used to obtain new non-standard Lagrangians for dissipative dynamical
systems in a simple and straightforward way. We exemplify the new method by
applying it to the case of the free particle and the simple harmonic oscillator
in order to obtain new non-standard Lagrangians for dissipative systems.
