Keypoint detection and description in a continuous scale space achieves better robustness to scale change than those in a discretized scale space. State-of-the-art methods first decompose a continuous scale space into M + 1 component images weighted by M-order polynomials of scale σ, and then reconstruct the value at an arbitrary point in the scale space by a linear combination of the component images. However, these methods create the mismatch that, if σ is large, common filter kernels such as Gaussian converge to zero; but the polynomials of σ diverge. This paper presents a more efficient approximation that suppresses this mismatch by normalizing the weighting functions. Experiments show that the proposed method achieves higher performance tradeoff than state-of-the-art methods: it reduces the number of component images and total running time by 20-40% without a sacrifice of stability in keypoints detection.