Abstract: Two properties are given in this paper about the scaling function: suppose V_j; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a₁,b₁]∪[a₂,b₂](b₁ < a₂,0 < a₂), then we havea1 ≤ 0, 0 < b₁, a₁ < b₂/2 ≤ b₁, 2π < b₂ - a₁ ≤ 8π.

Key words: multiresolution , analysis, scaling , function, Fourier , transform