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Direction of arrival estimation of wideband signals takes an important place in both literature and practical applications. Although there are several studies on this topic, behavior of non-uniform linear arrays (NLA) for wideband signals was not investigated comprehensively. In this paper performance of Root-MUSIC algorithm is studied for wideband signals using NLA and a new approach is proposed. This new approach decreases the mean square error of the arrival angle estimation using Wiener formulation and initial estimate of the arrival angles. Advantages of NLA use for wideband signals are presented via several simulations.