In this paper, the authors propose a new method for the design of fault tolerant linear state machines with initial state 0 and one dimensional input and one-dimensional output. It is shown that the LFSR-implementation of the transfer function of a linear automaton can be utilized to correct transient errors in the memory elements. Since, the state vector of a linear automaton is uniquely determined by the last n inputs and outputs, a transient error in a memory element can be corrected within n clock cycles by use of the corrected output symbols, where n is the number of components of the state vector.