A facial biometric template is a permanent identifier: once a stored template is exposed it cannot be reissued, so single-node storage is a critical point of failure. This work continues the authors' line of research on protecting facial templates with threshold secret sharing and develops a modified algorithm oriented specifically to facial biometrics. The starting point is a share-verifiable secret sharing scheme based on multivariable linear functions, originally proposed for general confidential data and not designed for biometrics. Its mathematical rule is changed: the pseudo-random coefficient matrix is replaced by a structured Vandermonde rule; blockwise packing of the protected facial record and masking are introduced; and the hash-based check is replaced by an unconditionally secure algebraic authentication code. The resulting block-packed secret sharing scheme is MDS (maximum distance separable - any k of n shares reconstruct the secret), perfectly secret up to the privacy threshold t, has exactly bounded ramp leakage and unconditional share verification; all properties are proven. Experimentally, with n = 7, k = 5 all 6300 subsets reconstructed without error; over a small field the modified scheme produced no singular subsets versus 0.41 % for the original; ramp leakage matched theory. For a 256-byte protected record, packing reduces total share storage 64-fold and halves verification metadata; unconditional share verification runs in 0.0012 ms. Recognition accuracy is inherited from the front end and is left unchanged by the protection layer: it reaches an EER (equal error rate) of 0.30 % in deep-embedding mode and 0.02 % in high-quality mode.