The magnetite composition from three sets of samples of Mazama, St. Helens set Y, and Bridge River tephras from Jasper and Banff national parks are used to test whether discriminant function analysis can unambiguously distinguish these tephras. The multivariate method is found to be very sensitive to the change in reference samples. St. Helens set Y tephra is clearly distinguished. However, discrimination between Mazama and Bridge River tephras is less distinct. A set of unknown tephras from the Sunwapta Pass area was used to test the classification schemes. Unknown tephras are assigned to different tephra types depending on which reference tephra set is used in the discriminant function analysis.