We determine the injective envelope and local multiplier algebra of a continuous trace C*-algebra <i>A</i> that arises from a continuous Hilbert bundle over an arbitrary locally compact Hausdorff space. In addition, we show that the second-order local multiplier algebra M<SUP>[2]</SUP><SUB>loc</SUB>(<i>A</i>) of any such algebra <i>A</i> is injective.Facultad de Ciencias Exactas