This paper presents a new local texture descriptor, Local Quaternary Patterns (LQP) and its extension, Feature Local Quaternary Patterns (FLQP). The LQP, which encodes four relationships of local texture, includes more information of local texture than the Local Binary Patterns (LBP) and Local Ternary Patterns (LTP). The FLQP which encodes both local and feature information is expected to perform better than the LQP for texture description and pattern recognition. To reduce the size of feature dimensions and histograms of both LQP and FLQP, a new coding schema is proposed to split the LQP and FLQP into two binary codes: the upper and lower binary codes. As a result, the total possible values of split LQP and FLQP are reduced to 512. The feasibility of the proposed LQP and FLQP methods is demonstrated on an eye detection problem. Experimental results using the BioID database show that both the FLQP and the LQP methods archive better performance than the feature LTP, the LTP, the feature LBP and the LBP methods. Specifically, the FLQP method achieves the highest eye detection rate among all the competing methods.