  We propose a possible mechanism of pseudo spin gap anomaly(PSGA) in
magnetically coupled bi-layer cuprates without any fermion pairing instability.
In our proposal PSGA does not necessarily require the spin-charge separation or
the breakdown of the Fermi liquid description of a normal state of the cuprate
superconductor.The low energy magnetic excitations are mainly governed by the
{\it itinerant nature of the intra-layer system} and {\it the inter-layer
antiferromagnetic coupling}. No matter how weak the bare inter-layer coupling
is, it can be dramatically enhanced due to the intra-layerspin fluctuations. As
the temperature decreases near the antiferromagnetic phase boundary the
strongly enhanced inter-layer correlation induces the inter-layer particle-hole
exchange scattering processes that tend to enhance the inter-layer spin singlet
formation and kill the triplet formation. We propose that the coupling of spin
fluctuations on the adjacend layers via the strong repulsive interaction
between parallel spins travelling on each layer give rise to the dynamical
screening effects. As a result the low energy part of the spin excitation
spectrum is strongly suppressed as the temperature decreases near the
antiferromagnetic phase boundary. We ascribe PSGA to this dynamical screening
effects.
