A metamorphic rock doesn't actually change into an igneous rock, as the process of melting results in a melt, which crystallizes into a completely different kind of rock, rather than a gradual transition in form and mineralogy. read more
This metamorphic rock can then be weathered at the surface and eroded, with the little pieces of metamorphic rock being deposited somewhere. With sufficient pressure of piling sediments, or tectonic pressures, these bits of ex-metamorphic rock may be pressed and cemented into a sedimentary rock. read more