1. A biometric authentication method comprising the steps of: extracting a feature data array for registration from biometric information of a registration applicant at a biometric information registration time by using a client; generating a first conversion parameter for comparison at the biometric information registration time by using the client, the first conversion parameter for comparison being used to convert the feature data array for registration; generating a position correction template from the feature data array for registration at the biometric information registration time by using the client; generating a comparison template by converting the feature data array for registration using the first conversion parameter for comparison at the biometric information registration time by using the client; transmitting the position correction template and the comparison template to a server at the biometric information registration time by using the client; extracting a feature data array for authentication from biometric information of a user at an authentication time by using the client; generating a second conversion parameter for comparison at the authentication time by using the client, the second conversion parameter for comparison being used to convert the feature data array for authentication; generating converted feature data for position correction from the feature data array for authentication at the authentication time by using the client; transmitting the converted feature data for position correction to the server at the authentication time by using the client; storing the position correction template and the comparison template transmitted by the client in a database coupled to the server by using the server; calculating a position correction amount between the feature data array for registration and the feature data array for authentication using the position correction template stored in the database and the converted feature data for position correction transmitted by the client by using the server; transmitting the position correction amount to the client by using the server; generating a corrected feature data array by performing position correction on the feature data array for authentication on the basis of the position correction amount by using the client; generating a converted feature data array for comparison by converting the corrected feature data array using the second conversion parameter for comparison by using the client; transmitting the converted feature data array for comparison to the server by using the client; calculating the distance between the comparison template stored in a database and the converted feature data array for comparison transmitted by the client by using the server; and determining success or failure of authentication of the user as the registration applicant on the basis of comparison between the distance and a predetermined authentication threshold by using the server.