We describe here a compact nonmagnetic composite high pressure cell of piston-cylinder type with inner diameter of 6 mm equipped with manganin pressure sensor. This cell was developed for room temperature measurements of magnetic remanence of relatively large rock samples (up to 5.8 mm in diameter and 15 mm long cylinders) under hydrostatic pressure up to 1.5 GPa (the operating pressure limit) in the 2G Enterprises superconducting quantum interference device magnetometer. Its design was focused on minimizing the remanent magnetic moment m(r) of the cell (m(r)=3 x 10(-8) A m(2)) that allowed direct measurements of remanent magnetic moment M(r) under pressure for weakly magnetic materials-rock samples (M(r) epsilon[5 x 10(-7),10(-4)] A m(2)). The inner part of this composite cell is made of hard "Russian alloy" (Ni(57)Cr(40)Al(3)) whereas the envelope of the cell corps is made of less magnetic titanium alloy. This design solution permitted to reduce the total remanent magnetic moment of the whole cell and represents the main device feature. We describe here the choice of materials for pressure cell based on their magnetic and mechanical properties, the choice of the pressure transmitting medium (polyethilsiloxane liquid) providing perfectly hydrostatic conditions for the sample as well as the cell geometry. The cell performance is illustrated by results of pressure demagnetization experiments on rocks and minerals.