Abstract: Based on the Element Energy Projection (EEP) method, the present paper presents, for one-dimensional C⁰ FEM, an improved scheme with optimal order of super-convergence, i.e., FEM sulotions can be obtained through the scheme for the elements with sufficient smooth property and m degrees. The proposed scheme is capable of producingO(h^2m) super-convergence for both displacements and stresses at any point on an element in post-processing stage. To achieve that, the concept of condensed shape functions was developed and the associated theorems of approximation and equivalence were proved. The whole work consists of three parts, i.e., formulation, numerical results and mathematical analysis. The present paper is the first in the series and gives the formulation of the proposed scheme.