An important property of apodized weak fiber Bragg grating ;FBG is demonstrated.It shows that if the reflection spectra R;Δβ of an apodized weak FBG is needed to be narrowed to ′1/n′,i.e.from R;Δβ to R;nΔβ,then the apodizing function g;z should be broadened ′n′ times,i.e.from g;z 0