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In this paper, we study the finite Hankel transformation on spaces of generalized functions by developing a new procedure. We consider two Hankel type integral transformations $h_{\mu }$ and $h_{\mu }^{*}$ connected by the Parseval equation $$\sum _{n=0}^{\infty }\left(h_{\mu }f\right)\left(n\right)\left(h_{\mu }^{*}\varphi \right)\left(n\right)={\int }_0^{1}f\left(x\right)\varphi \left(x\right)dx.$$ A space $S_{\mu }$ of functions and a space $L_{\mu }$ of complex sequences are introduced. $h_{\mu }^{*}$ is an isomorphism from $S_{\mu }$ onto $L_{\mu }$ when $\mu \ge -\frac{1}{2}$. We propose to define the generalized finite Hankel transform $h_{\mu }^{\text{'}}f$ of $f\in S_{\mu }^{\text{'}}$ by $$\langle \left(h_{\mu }^{\text{'}}f\right),{\left(\left(h_{\mu }^{*}\varphi \right)\left(n\right)\right)}_{n=0}^{\infty }\rangle =\langle f,\varphi \rangle ,\text{for}\varphi \in S_{\mu }.$$