We studied the dielectric properties of Al2O3-MgO-ReOx (Re: rare earth) systems in the microwave region and found that the magnetoplumbite phases in the MgO-poor regions of MgReAl11O19 (Re: La ∼ Tb) compositions had positive TCF (temperature coefficient of resonance frequency) values in spite of having low dielectric constants of under 20. By mixing a lead-free glass with the above system, a novel LTCC (which we term an AMSG) was obtained that was characterized by a low dielectric constant (< 10), a near zero TCF, and high bending strength. When firing these AMSG green sheets inserted between HTCC alumina or magnesia green sheets that cannot be sintered at the AMSG sintering temperature, the AMSG sheets were seen to shrink not in the x-y directions but in the z direction due to the constraining effects of the HTCC layers. The obtained non-shrinkage substrate had precise dimensions and a high degree of flatness. The AMSG and the non-shrinking techniques have potential for application to integrated RF modules in mobile communications equipment.