Recently, Elamir and Seheult (2003) introduced TL-moments as an extension of L-moments that depend on giving zero weight to extreme observations. TL-moments give more robust estimators than L-moments in the presence of outliers. Moreover, population TL-moments may be well defined where the corresponding population L-moments do not exist. Also, they discussed TL-moments when t (number of trimmed observations) is an integer number. The aim of this study is to extend the value of t from integer numbers to fractional numbers by introducing a new linear method of estimation which may be called...