Estimating different characteristics viz., size, cost, etc. of software during different phases of software development is required to manage the resources effectively. Function points measure can be used as an input to estimate these characteristics of software. The Traditional Function Point Counting Procedure (TFPCP) cannot be used to measure the functionality of an Object Oriented (OO) system. This paper suggests a counting procedure to measure the functionality of an OO system during the design phase from a designers' perspective. It is adapted from the TFPCP. The main aim of this paper is to use all the available information during the OO design phase to estimate Object Oriented Design Function Points (OODFP). The novel feature of this approach is that it considers all the basic concepts of OO systems such as inheritance, aggregation, association and polymorphism.