  Gamma-ray bursts (GRBs) are among the most powerful sources in the universe.
In the recent years, GRBs have been proposed as a complementary probe to type
Ia supernovae (SNIa). However, as is well known, there is a circularity problem
in the use of GRBs to study cosmology. In this work, based on the Pad\'e
approximant, we propose a new cosmology-independent method to calibrate GRBs.
We consider a sample consisting of 138 long Swift GRBs and obtain 79 calibrated
long GRBs at high-redshift $z>1.4$ (named Mayflower sample) which can be used
to constrain cosmological models without the circularity problem. Then, we
consider the constraints on several cosmological models with these 79
calibrated GRBs and other observational data. We show that GRBs are competent
to be a complementary probe to the other well-established cosmological
observations.
