Some of the authors have reported that a complex hydride, Li(BH4), with the (BH4)(-) anion exhibits lithium fast-ion conduction (more than 1 x 10(-3) S/cm) accompanied by the structural transition at similar to 390 K for the first time in 30 years since the conduction in Li-2(NH) was reported in 1979. Here we report another conceptual study and remarkable results of Li-2(BH4)(NH2) and Li-4(BH4)(NH2)(3) combined with the (BH4)(-) and (NH2)(-) anions showing ion conductivities 4 orders of magnitude higher than that for Li(BH4) at RT, due to being provided with new occupation sites for Li+ ions. Both Li-2(BH4)(NH2) and Li-4(BH4)(NH2)(3) exhibit a lithium fast-ion conductivity of 2 x 10(-4) S/cm at RT, and the activation energy for conduction in Li-4(BH4)(NH2)(3) is evaluated to be 0.26 eV, less than half those in Li-2(BH4)(NH2) and Li(BH4). This study not only demonstrates an important direction in which to search for higher ion conductivity in complex hydrides but also greatly increases the material variations of solid electrolytes.