Based upon the proposition that the roles of inputs and outputs in a physical system and those in the corresponding output-injection observer do not really have to be consistent, a systematic procedure is developed in this work to properly divide a set of sparse system models and measurement models into a number of independent subsets with the help of a visual aid. Several smaller sub-observers can then be constructed accordingly to replace the original one. The size of each sub-observer may be further reduced by strategically selecting one or more appended states. These techniques are shown to be quite effective in relieving on-line computation load of the output-injection observers and also in identifying detectable sub-systems.