diff --git a/specs/altair/beacon-chain.md b/specs/altair/beacon-chain.md
index aa1509460..a69412c31 100644
--- a/specs/altair/beacon-chain.md
+++ b/specs/altair/beacon-chain.md
@@ -281,11 +281,12 @@ def get_sync_committee_indices(state: BeaconState, epoch: Epoch) -> Sequence[Val
     Note: This function is not stable during a sync committee period as
     a validator's effective balance may change enough to affect the sampling.
     """
+    assert epoch % EPOCHS_PER_SYNC_COMMITTEE_PERIOD == 0
+
     MAX_RANDOM_BYTE = 2**8 - 1
-    base_epoch = Epoch((max(epoch // EPOCHS_PER_SYNC_COMMITTEE_PERIOD, 1) - 1) * EPOCHS_PER_SYNC_COMMITTEE_PERIOD)
-    active_validator_indices = get_active_validator_indices(state, base_epoch)
+    active_validator_indices = get_active_validator_indices(state, epoch)
     active_validator_count = uint64(len(active_validator_indices))
-    seed = get_seed(state, base_epoch, DOMAIN_SYNC_COMMITTEE)
+    seed = get_seed(state, epoch, DOMAIN_SYNC_COMMITTEE)
     i = 0
     sync_committee_indices: List[ValidatorIndex] = []
     while len(sync_committee_indices) < SYNC_COMMITTEE_SIZE:
@@ -689,6 +690,7 @@ def process_participation_flag_updates(state: BeaconState) -> None:
 def process_sync_committee_updates(state: BeaconState) -> None:
     next_epoch = get_current_epoch(state) + Epoch(1)
     if next_epoch % EPOCHS_PER_SYNC_COMMITTEE_PERIOD == 0:
+        print("HEEEREEE")
         state.current_sync_committee = state.next_sync_committee
         state.next_sync_committee = get_sync_committee(state, next_epoch)
 ```
@@ -735,8 +737,13 @@ def initialize_beacon_state_from_eth1(eth1_block_hash: Bytes32,
     state.genesis_validators_root = hash_tree_root(state.validators)
 
     # [New in Altair] Fill in sync committees
-    state.current_sync_committee = get_sync_committee(state, get_current_epoch(state))
-    state.next_sync_committee = get_sync_committee(state, get_current_epoch(state) + EPOCHS_PER_SYNC_COMMITTEE_PERIOD)
+    current_period = get_current_epoch(state) // EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+    previous_period = current_period - min(1, current_period)
+    current_base_epoch = current_period * EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+    previous_base_epoch = previous_period * EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+
+    state.current_sync_committee = get_sync_committee(state, previous_base_epoch)
+    state.next_sync_committee = get_sync_committee(state, current_base_epoch)
 
     return state
 ```
diff --git a/tests/core/pyspec/eth2spec/test/altair/block_processing/test_process_sync_committee.py b/tests/core/pyspec/eth2spec/test/altair/block_processing/test_process_sync_committee.py
index 2e5d62d11..48e556f50 100644
--- a/tests/core/pyspec/eth2spec/test/altair/block_processing/test_process_sync_committee.py
+++ b/tests/core/pyspec/eth2spec/test/altair/block_processing/test_process_sync_committee.py
@@ -345,10 +345,10 @@ def test_valid_signature_future_committee(spec, state):
     transition_to(spec, state, slot_in_future_sync_committee_period)
 
     sync_committee = state.current_sync_committee
+    next_sync_committee = state.next_sync_committee
+    expected_next_sync_committee = spec.get_sync_committee(state, epoch_in_future_sync_committee_period)
 
-    expected_sync_committee = spec.get_sync_committee(state, epoch_in_future_sync_committee_period)
-
-    assert sync_committee == expected_sync_committee
+    assert next_sync_committee == expected_next_sync_committee
     assert sync_committee != old_current_sync_committee
     assert sync_committee != old_next_sync_committee
 
diff --git a/tests/core/pyspec/eth2spec/test/altair/epoch_processing/test_process_sync_committee_updates.py b/tests/core/pyspec/eth2spec/test/altair/epoch_processing/test_process_sync_committee_updates.py
index c909c791c..ca25797c4 100644
--- a/tests/core/pyspec/eth2spec/test/altair/epoch_processing/test_process_sync_committee_updates.py
+++ b/tests/core/pyspec/eth2spec/test/altair/epoch_processing/test_process_sync_committee_updates.py
@@ -40,7 +40,7 @@ def run_sync_committees_progress_test(spec, state):
     # Can compute the third committee having computed final balances in the last epoch
     # of this `EPOCHS_PER_SYNC_COMMITTEE_PERIOD`
     current_epoch = spec.get_current_epoch(state)
-    third_sync_committee = spec.get_sync_committee(state, current_epoch + 2 * spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD)
+    third_sync_committee = spec.get_sync_committee(state, current_epoch + 1)
 
     assert state.current_sync_committee == second_sync_committee
     assert state.next_sync_committee == third_sync_committee
diff --git a/tests/core/pyspec/eth2spec/test/helpers/genesis.py b/tests/core/pyspec/eth2spec/test/helpers/genesis.py
index 4a34a5eb3..23cd04c93 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/genesis.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/genesis.py
@@ -69,9 +69,12 @@ def create_genesis_state(spec, validator_balances, activation_threshold):
 
     if spec.fork not in FORKS_BEFORE_ALTAIR:
         # Fill in sync committees
-        state.current_sync_committee = spec.get_sync_committee(state, spec.get_current_epoch(state))
-        state.next_sync_committee = (
-            spec.get_sync_committee(state, spec.get_current_epoch(state) + spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD)
-        )
+        current_period = spec.get_current_epoch(state) // spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+        previous_period = current_period - min(1, current_period)
+        current_base_epoch = current_period * spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+        previous_base_epoch = previous_period * spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+
+        state.current_sync_committee = spec.get_sync_committee(state, previous_base_epoch)
+        state.next_sync_committee = spec.get_sync_committee(state, current_base_epoch)
 
     return state