A numerical method is developed which handles the Mellin transform (1) \(M_{\epsilon}(y;f)=\int^{\infty}_{0}x^{-iy-\epsilon}f(x)dx,y\in [0,\infty),\epsilon \geq 0,i=\sqrt{\quad -1}\) of a Fourier-bandlimited function f(x). Denoting \(F(z)(F(z)=0\) for \(z\geq Z_ 0)\) the Fourier transform of the even continuation of f(x), then instead of (1) one can take (2) \(M_{\epsilon}(y;f)=\int^{\infty}_{0}z^{iy+\epsilon - 1}F(z)dz=\int^{Z}_{0}z^{iy+\quad \epsilon -1}F(z)dz\), \(Z\geq Z_ 0\) because \(M'_{\epsilon}(y;f)=h_{\epsilon}(y)M_{\epsilon}(y;f)\) holds \((h_{\epsilon}(y)\) is a function independent on f). In view of the sampling theorem F(z) may be represented by the Fourier series \(F(z)=\Delta x\{f(0)+2\sum^{\infty}_{n=1}\cos (2\pi zn\Delta x)\) f(n\(\Delta\) x)\(\}\) provided that \(\Delta\) \(x\leq 1/(2Z)\). Substituting this into (2) we arrive at (3) \(M_{\epsilon}(y;f)=\sum^{\infty}_{n=0}\psi_{\epsilon,n}(y)f(n\Delta x)\) [\textit{M. H. Brill} and the author, Elektron. Informationsverarbeitung Kybernetik 20, 229-233 (1984; Zbl 0557.65085)]. The author suggests a modification of the Mellin kernel \(z^{iy+\epsilon -1}\) in the interval \((Z_ 0,Z]\) to improve convergence properties of (3). Moreover, the convergence may be controlled because it becomes faster with growing \(\epsilon\) and Z (or sampling frequency). Numerical examples are included which illustrate that 50 to 100 terms of (3) are sufficient if \(\epsilon =2\) and \(Z=2Z_ 0\). The required \(\psi_{\epsilon,n}\) are independent on f and may be precomputed within a machine precision. The presented method may enhance the utility of the Mellin transform in scale-invariant pattern recognition.