  In this paper, we propose a new approach to the investigation of asymptotic
properties of trimmed $L$-statistics and we apply it to the Cram\'{e}r type
large deviation problem. Our results can be compared with ones in Callaert et
al.(1982) -- the first and, as far as we know, the single article, where some
results on probabilities of large deviations for the trimmed $L$-statistics
were obtained, but under some strict and unnatural conditions. Our approach is
to approximate the trimmed $L$-statistic by a non-trimmed $L$-statistic (with
smooth weight function) based on Winsorized random variables. Using this
method, we establish the Cram\'{e}r type large deviation results for the
trimmed $L$-statistics under quite mild and natural conditions.
