A framework for oversampled filter banks for graph signals was recently proposed by Tanaka and Sakiyama (2014). It was shown that M-channel oversampled filter bank which is exactly orthogonal is not possible with polynomial spectral filter functions. The result is an extension of the critically sampled framework of Narang and Ortega (2012). In this work we present a solution that is nearly orthogonal which has the advantage of giving a nearly tight transform, i.e. nearly equal frame bounds. A family of target functions which satisfy the orthogonality condition is constructed using Bernstein polynomials. The design of the spectral filters is easily achieved through an approximation of the target functions. Filters with good spectral characteristics that are nearly orthogonal can be easily obtained using the proposed method.