Random projection is a technique which was first used for data compression, by using a matrix with random variables to map a high dimensional vector to a lower dimensional one. The lower dimensional vector preserves certain properties of the higher dimensional vector, up to a certain degree of accuracy. However, random projections can also be used for matrix decompositions and factorizations, described in [1]. We propose a new structure of random projections, and apply this to the method of recovering principal components, building upon the work of Anaraki and Hughes [2]. Our extension results in a better accuracy in recovering principal components, as well as a substantial saving in storage space. Experiments have been conducted on both artificial data and on the MNIST dataset to demonstrate our results.