Abstract : We introduce a variation of the discrete-time quantum walk, the nonreversal quantum walk, which does not step back onto a position that it has just occupied. This allows us to simulate a dimer and we achieve it by introducing a different type of coin operator. The nonrepeating walk, which never moves in the same direction in consecutive time steps, arises by a permutation of this coin operator. We describe the basic properties of both walks and prove that the even-order joint moments of the nonrepeating walker are independent of the initial condition, being determined by five parameters derived from the coin instead. Numerical evidence suggests that the same is the case for the nonreversal walk. This contrasts strongly with previously studied coins, such as the Grover operator, where the initial condition can be used to control the standard deviation of the walker.