For applications of wireless communication of the fourth generation (4G LTE), the technique of using a printed parallel-resonant spiral strip for bandwidth enhancement of a small-size planar laptop computer (especially the thin Ultrabook) antenna for the LTE operation is first presented. The antenna is printed on a thin FR4 substrate of small size 45 x 9 mm2 with a simple uniplanar structure which is promising for Ultrabook application. Based on the proposed antenna structure, its application for MIMO operation to achieve enhanced isolation is also analyzed in this thesis. Different from the works for the relatively much smaller ground plane conditions such as in the mobile phones, the effect of different size of the supporting conductive plate of the upper corner of the Ultrabook is discussed for the isolation issue of the MIMO antennas. Finally, the technique of isolation improvement in the LTE700 band for the MIMO operation in the Ultrabook is presented.