We present new results from a ground-based program to determine the proper motion of the Magellanic Clouds (MCs) relative to background quasars (QSOs), being carried out with the Iréneé du Pont 2.5 m telescope at Las Campanas Observatory, Chile. The data were secured over a time base of seven years and with eight epochs of observation "As measured" (field) proper motions were obtained for five QSO fields in the Small Magellanic Cloud (SMC): QJ0033-7028, QJ0035-7201, QJ0047-7530, QJ0102-7546, and QJ0111-7249. Assuming that the SMC has a disklike central structure, but that it does not rotate, we determined a center-of-mass (CM) proper motion for the SMC from two of these fields, QJ0033-7028 and QJ0035-7201, located to the northwest and west of the main body of the SMC, respectively. Combining these latter proper motions with the CM proper motion presented by Costa et al. (hereafter CMP09) for the SMC (from the field QJ0036-7227, located to the west of the main body of the SMC), we obtain a weighted mean of μα cos δ = +0.93 ± 0.14 mas yr-1 and μδ = -1.25 ± 0.11 mas yr-1. This CM proper motion is in good agreement with recent results by Piatek et al. and Vieira et al., and we are confident that it is a good representation of the "bulk" transverse motion of the SMC. On the contrary, the results we obtain from the fields QJ0047-7530 and QJ0102-7546, located to the south of the main body of the SMC, and the field QJ0111-7249, located to the east of its main body, seem to be affected by streaming motions. For this reason, we have not used the latter to determine the SMC CM proper motion. These streaming motions could be evidence that the SMC was tidally disrupted in a close encounter with the Large Magellanic Cloud (LMC). Complementing the SMC CM proper motions given here and in CMP09, with the currently accepted radial velocity of its center, we have derived its galactocentric (gc) velocity components, obtaining a weighted mean of V gc,t = +289 ± 25 km s-1 and V gc,r = +14 ± 24 km s-1. These velocities, together with the galactocentric velocity components given for the LMC in CMP09, imply a relative velocity between the LMC and SMC of 67 ± 42 km s-1 for V rot,LMC = 50 km s-1 and of 98 ± 48 km s-1 for V rot,LMC = 120 km s-1. Despite our large errors, these values are consistent with the standard assumption that the MCs are gravitationally bound to each other.