Let \(\Lambda\) be an associative algebra over a field, \(A\) a subalgebra of \(\Lambda\), and \(M\) a two-sided ideal of \(\Lambda\) such that \(\Lambda\simeq A\oplus M\). The authors study Hochschild cohomology of \(\Lambda\) by constructing and studying a long exact sequence relating Hochschild cohomology of \(\Lambda\) and cohomology of \(A\) and \(M\).