In the context of model-based failure detection and diagnosis, there i
s a residual generation which can be obtained through a generalized pa
rity space concept. This paper presents a new algorithm involving the
generation of redundancy or parity equations for dynamic linear time-i
nvariant systems. The proposed scheme involves the successive eliminat
ion of state sub-vectors and their replacement by output values as wel
l as the processing of an output done one at a time to avoid matrix in
version. Some examples point out the numerical efficiency of the propo
sed procedure.