  We present the results of our extensive search using the Bayesian block
method for long tails following short bursts from a magnetar, SGR J1550-5418,
over all RXTE observations of the source. We identified four bursts with
extended tails, most of which occurred during its 2009 burst active episode.
The durations of tails range between ~13 s and over 3 ks, which are much longer
than the typical duration of bursts. We performed detailed spectral and
temporal analysis of the burst tails. We find that the spectra of three tails
show a thermal nature with a trend of cooling throughout the tail. We compare
the results of our investigations with the properties of four other extended
tails detected from SGR 1900+14 and SGR 1806-20 and suggest a scenario for the
origin of the tail in the framework of the magnetar model.
