Abstract: Finite volume methods (such as k-exact, WENO, compact reconstruction, etc) for the two-dimensional Euler equations require time-consuming piecewise two-dimensional (2D) reconstruction unexceptionally. It is found that this 2D reconstruction is used only for evaluating flow variables at Gauss points for calculating numerical fluxes, so the 2D reconstruction seems to be unnecessary. Inspired by this observation, it was proposed to use one-dimensional (1D) reconstruction on the side of a cell to replace the 2D reconstruction on the cell as is the case with finite volume method. For the 2D Euler equations on uniform rectangular grids and unstructured triangular grids a new numerical method (termed as lowered dimension reconstruction algorithm) was developed. Numerical examples show that this algorithm can be used to compute inviscid flow problems with strong shock waves and has good computational efficiency.