  In this paper we study decoherence in the quantum walk on the line. We
generalize the method of decoherent coin quantum walk, introduced by Brun et al
[Phys. Rev. A {\bf 67}, 32304 (2003)]. Our analytical expressions are
applicable for all kinds of decoherence. As an example of the coin-position
decoherence, we study the broken line quantum walk and compare our results with
the numerical one. We also show that our analytical results reduce to the Brun
formalism when only the coin is subjected to decoherence.
