The LIE algebra U of the invariance group of any field theory with a homogeneous quadratic Lagrangian shows a remarkable structure: If D1, D2, D3 are any three elements of U then the expression ½ (D1 D2 D3 +D3 D2 D1) also belongs to U. This general property allows, starting with known invariance transformations or conservation laws, to derive an infinite number of conservation laws.