This paper presents an alternative formulation of invariant moments using higher order centralised scaled-invariants for unequal scaling unconstrained handwritten digits which undergo basic transformations. Basic transformations that are covered in this study includes scaling and rotation embedded into Hu's invariants. Moment invariants have been proposed as pattern sensitive features in classification and recognition applications. Hu was the first to introduce the concept of invariants based on combinations of regular moments using algebraic invariants. In this study, we consider unconstrained handwritten digits of different presentations. Results of computer simulations for digits of unequal scaling are also included verifying the validity of the method proposed.