This paper discusses observer design for unforced non-linear multi-output systems using a block triangular observer form (BTOF). The BTOF allows an established exact error linearization observer design method to be generalized to a larger class of multi-output systems. Observer design proceeds in a decentralized manner, or subsystem-at-a-time, starting with the uppermost subsystem. Designs for each subsystem effectively treat upper subsystem states as known measurements and are relatively simple given their reduced dimension. Exponential error stability results are given. New necessary and sufficient existence conditions are given for the BTOF. Examples illustrate the construction of the BTOF coordinates and the advantages of a BTOF-based design compared to a generally applicable method.