Parameter-free locality preserving projection does not need to set parameters and has stable performance, but the algorithm cannot effectively maintain the local structure of the sample and ignores the role of non-local samples. Moreover, this method exists the Small Size Sample (SSS) problem. A complete parameter-free local neighborhood preserving and non-local maximization algorithm was proposed. In order to make full use of the nearest neighbor samples and non-nearest neighbor samples, which were divided by whether the distance between two samples is no more than 0.5 or not, the neighbor scatter matrix and non-nearest neighbor scatter matrix were constructed. Then, the objective function of the algorithm was to seek a set of projection vectors such that the neighbor scatter matrix was maximized and non-nearest neighbor scatter matrix was minimized simultaneously. As to solve the objective function, the high dimensional samples were projected to a low dimensional subspace by Principal Component Analysis (PCA) algorithm, which was proved without lossing any effective discriminant information according to two theorems. In order to solve the SSS problem, the objective function was converted to differential form. The experimental results on face database and palmprint database illustrate that the proposed method outperforms Parameter-free locality preserving projection with average recognition rate, which proves the effectiveness of the proposed algorithm.