Fingerprint analysis plays a crucial role in crucial legal matters such as investigation of crime andsecurity system. Due to the large number and size of fingerprint images, data compression has to be applied to reduce the storage and communication bandwidth requirements of those images. To do this, there are many types of wavelet has been used for fingerprint image compression where some wavelet families exists such as Symlets, Daubechies and Coiflets etc. and one may use different types of wavelet to compress fingerprint images or any other images. We would like to say that if we wish to compress fingerprint images or any other images by using a member of a wavelet family, then it would be better to use such a member who will give much better result among all members of that family. According to this, to find most useful member from Coiflet's wavelet family we have made an experiment on this family by compressing a fingerprint image.