Summary: All finite-dimensional indecomposable solvable Lie algebras \(L(n,f)\), having the triangular algebra \(T(n)\) as their nilradical, are constructed. The number of non-nilpotent elements \(f\) in \(L(n,f)\) satisfies \(1\leq f\leq n-1\) and the dimension of the Lie algebra is \(\dim L(n,f)= f+ \frac 12 n(n-1)\).