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This paper studies an efficient method of identification of dynamic properties such as natural frequencies of, modal damping coefficients flL and participation factors p at the a-th mass, of a multiple degree of freedom linear system on the bases of using microtremor records which are measured at the first floor and at the roof in a fourstorey reinfoced concrete building. The EK-WGI method which was previously proposed by the present authors is used for the solution of a system identification problem, As a result, dynamic properties of the first mode and the second mode can be estimated from this method. Then, it is found that this method is more useful tool for the identification than the response function which is a common approach to estimate dynamic properties.