The author considers an arrangement \(\mathcal A\) of hyperplanes in \(\mathbb{C}^ d\). He computes the cohomology of a perverse sheaf \({\mathbf P}^ \bullet\) on \(\mathbb{C}^ d\) which is constructible with respect to the stratification determined by \(\mathcal A\) (call \(X\) this stratified space). He constructs a differential complex \({\mathbf K}^ \bullet({\mathbf P}^ \bullet)\) whose cohomology is isomorphic to \(H^*(X;{\mathbf P}^ \bullet)\), the cohomology of the sheaf \({\mathbf P}^ \bullet\). The main point is that this complex is directly calculated from any weakly self-indexing Morse function of \(X\) (a particular case of Morse function on a stratified space). Two particular cases are developed, where \({\mathbf V}\) is a local coefficient system on the complement \(M = \mathbb{C}^ d - \bigcup_{H\in{\mathcal A}}H\) of \(\mathcal A\): 1) When the perverse sheaf \({\mathbf P}^ \bullet\) is the direct image of \({\mathbf V}\) under the natural inclusion \(i: M\to X\), the complex \({\mathbf K}^ \bullet({\mathbf P}^ \bullet)\) calculates the cohomology \(H^*(M;{\mathbf V})\). 2) If the perverse sheaf \({\mathbf P}^ \bullet\) is taken to be \({\mathbf I}^{\overline{p}}{\mathbf C}^ \bullet({\mathbf V})\), the complex of sheaves of intersection cochains with coefficients in the local system \({\mathbf V}\), the complex \({\mathbf K}^ \bullet({\mathbf P}^ \bullet)\) calculates the intersection cohomology \(I^{\overline{p}}H^*(M;{\mathbf V})\). If the local system \({\mathbf V}\) is trivial then, the formula for the Betti numbers of \(M\) due to \textit{Orlik} and \textit{Solomon} is recovered. The work ends by giving some vanishing theorems for general position arrangements.