The uniqueness of shape and style of handwriting can be used for author’s authentication. Acquiring individual features to obtain Authorship Invarianceness Concept have led to an important research in Writer Identification domain. This paper discusses the investigation of this concept by extracting individual features using Geometric Moment Function. Experiment results have shown that Handwriting Invarianceness are discerning with better identification accuracy. This has verified that Moment Function is worth to be explored in identifying the handwritten authorship for Writer Identification.