diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index d5e978afb0..b7a63b4f69 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -284,7 +284,7 @@ These configurations are updated for releases, but may be out of sync during `de
 
 ## Data structures
 
-The following data structures are defined as [SimpleSerialize (SSZ)](https://github.com/ethereum/eth2.0-specs/blob/master/specs/simple-serialize.md) objects.
+The following data structures are defined as [SimpleSerialize (SSZ)](../simple-serialize.md) objects.
 
 The types are defined topologically to aid in facilitating an executable version of the spec.
 
@@ -657,11 +657,11 @@ Note: We aim to migrate to a S[T/N]ARK-friendly hash function in a future Ethere
 
 ### `hash_tree_root`
 
-`def hash_tree_root(object: SSZSerializable) -> Bytes32` is a function for hashing objects into a single root utilizing a hash tree structure. `hash_tree_root` is defined in the [SimpleSerialize spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/simple-serialize.md#tree-hash).
+`def hash_tree_root(object: SSZSerializable) -> Bytes32` is a function for hashing objects into a single root utilizing a hash tree structure. `hash_tree_root` is defined in the [SimpleSerialize spec](../simple-serialize.md#merkleization).
 
 ### `signing_root`
 
-`def signing_root(object: SSZContainer) -> Bytes32` is a function defined in the [SimpleSerialize spec](https://github.com/ethereum/eth2.0-specs/blob/dev/specs/simple-serialize.md#self-signed-containers) to compute signing messages.
+`def signing_root(object: SSZContainer) -> Bytes32` is a function defined in the [SimpleSerialize spec](../simple-serialize.md#self-signed-containers) to compute signing messages.
 
 ### `get_temporary_block_header`
 
@@ -1270,15 +1270,15 @@ def get_delayed_activation_exit_epoch(epoch: Epoch) -> Epoch:
 
 ### `bls_verify`
 
-`bls_verify` is a function for verifying a BLS signature, defined in the [BLS Signature spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/bls_signature.md#bls_verify).
+`bls_verify` is a function for verifying a BLS signature, defined in the [BLS Signature spec](../bls_signature.md#bls_verify).
 
 ### `bls_verify_multiple`
 
-`bls_verify_multiple` is a function for verifying a BLS signature constructed from multiple messages, defined in the [BLS Signature spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/bls_signature.md#bls_verify_multiple).
+`bls_verify_multiple` is a function for verifying a BLS signature constructed from multiple messages, defined in the [BLS Signature spec](../bls_signature.md#bls_verify_multiple).
 
 ### `bls_aggregate_pubkeys`
 
-`bls_aggregate_pubkeys` is a function for aggregating multiple BLS public keys into a single aggregate key, defined in the [BLS Signature spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/bls_signature.md#bls_aggregate_pubkeys).
+`bls_aggregate_pubkeys` is a function for aggregating multiple BLS public keys into a single aggregate key, defined in the [BLS Signature spec](../bls_signature.md#bls_aggregate_pubkeys).
 
 
 ### Routines for updating validator status