Unbiased quantum walk corresponds to the classical asymmetric random walk in quantum world, and asymmetry is reflected by coin operation and conditional walk. The basic properties of unbiased quantum walk are characterized by calculating its position probability distribution, the probability and mean value back to the origin. Numerical results show that the recurrence property of unbiased quantum walk in one-dimensional chain is independent of the selection of coin initial state and whether the distribution after evolution is symmetric, but only related to asymmetric operation. One-dimensional classical random walk is recoverable only when it is distributed symmetrically. Different from classical random walk, it is one of the remarkable characteristics of quantum walk.