Arbitrary N th-order (N ≥ 2) lensless ghost imaging with thermal light has been performed for the first time by only recording the intensities in two optical paths. It is shown that the image visibility can be dramatically enhanced as the order N increases. It is also found that longer integration times are required for higher-order correlation measurements as N increases, due to the increased fluctuations of higher-order intensity correlation functions.PACS numbers: 42.50. Dv, 42.25.Hz, 42.50.St Compared with the first "ghost" imaging experiment with two-photon entangled light [1], second-order ghost imaging and ghost interference with thermal light [2,3,4,5,6,7,8,9,10,11] has a low visibility which theoretically can never exceed 1/3, and in fact will be much lower than 1/3 in practical applications. Moreover, when a 2-dimensional high resolution image of a complex object is required, the better the resolution, the worse will its visibility be. This is one of the limitations for the practical application of thermal ghost imaging (GI). Fortunately, recent studies [12,13,14,15,17,18] on the higher-order intensity correlation effects of thermal light show that the visibility can be significantly improved by increasing the order N . In this way, the drawback of low visibility in correlated imaging with thermal light can be overcome.Third-order GI with thermal light has been theoretically analyzed to a certain extent [12,19], but recently Liu et al pointed out that it is inappropriate to assume that second-order correlations play the entire or dominant role [13]. In their investigations of higher-order thermal ghost imaging and interference Liu et al showed that it is N -photon bunching that characterizes the N thorder correlation and leads to the high-visibility in N thorder schemes. The necessary condition for achieving a ghost image or interference pattern in N th-order intensity correlation measurements is the synchronous detection of the same light field by different reference detectors. Multi-photon interference experiments have been carried out by Agafonov et al [14], verifying the conclusion that the visibility limits of three-photon and four-photon interference are respectively 82% and 94% for classical coherent light, as predicted theoretically by Richter [15]. Cao et al discussed N -th order intensity correlation in double-slit ghost interference with thermal light and proposed a scheme to study the visibility and resolution of the fringes with two detectors [17]. However, in their actual experiment only one CCD detector was employed, and the measurements were taken first with and then without the double-slit in place. Similar * Corresponding author: wula@aphy.iphy.ac.cn high-order schemes to obtain higher visibility but for GI were also suggested by Agafonov et al a little earlier [18].In this paper we report the first demonstration of an arbitrarily high N th-order lensless GI experiment with pseudothermal radiation. We do not actually need N light paths but measure the N th-order intensity correlati...