The verifiable necessary and sufficient conditions for the multioutput observer error linearization problem have not been found over the last three decades. In this technical note, we give the unverifiable necessary and sufficient conditions which are more specific than the ones in the literature. Using these conditions, a verifiable sufficient condition (also necessary with additional restriction on the problem) is derived. Since our proofs are constructive, a desired state transformation can also be found in the theorem. Also our algorithmic conditions can be easily implemented by a MATLAB programming.