The author gives a classification of connected n-dimensional Lorentz manifolds M which admit an isometry group G of dimension \(\binom{n}{2}+1\), \(n\geq 5\), with compact isotropy subgroups. The result is that M is one of the following five spaces: (i) \(M={\mathbb{R}}\times N\) with metric \(-dt^ 2+ds^ 2_ N\), and \(G=S^ 1\times I^ 0(N)\), (ii) \(M=S^ 1\times N\) with metric \(-d\theta^ 2+d\epsilon^ 2_ N\), and \(G=S^ 1\times I^ 0(N)\), (iii) \(M={\mathbb{R}}\times P\) with metric \(-dt^ 2+ds^ 2_ p\), and \(G={\mathbb{R}}\times I^ 0(N)\), (iv) \(M=S^ 1\times P\) with metric \(-d\theta +ds^ 2_ P\), and \(G=S^ 1\times I^ 0(P)\), or (v) \(M=U_ n^{-1}=\{(u_ 1,...u_ n);u_ n>0\}\) with metric \(ds^ 2_-=(-du^ 2_ 1+du^ 2_ 2+...+du^ 2_ n)/(cu_ n)^ 2\) and \(G=I^ 0(U^-_ n)\). Here N is a simply connected \((n-1)\) dimensional Riemannian manifold and P is \((n-1)\) dimensional real projective space. Their corresponding metrics are \(ds^ 2_ N\) and \(ds^ 2_ P\), and \(I^ 0(\cdot)\) denotes the identity component of the full isometry group of \((\cdot)\).