The paper presents an algorithm, UFLIC (Unsteady Flow LIC), to visualize vector data in unsteady flow fields. Using line integral convolution (LIC) as the underlying method, a new convolution algorithm is proposed that can effectively trace the flow's global features over time. The new algorithm consists of a time-accurate value depositing scheme and a successive feedforward method. The value depositing scheme accurately models the flow advection, and the successive feedforward method maintains the coherence between animation frames. The new algorithm can produce time-accurate, highly coherent flow animations to highlight global features in unsteady flow fields. CFD scientists, for the first time, are able to visualize unsteady surface flows using the algorithm.